BACKGROUND Esophageal stricture ranks among the most significant complications following endoscopic submucosal dissection(ESD).Excessive fibrotic repair is a typical pathological feature leading to stenosis after ESD....BACKGROUND Esophageal stricture ranks among the most significant complications following endoscopic submucosal dissection(ESD).Excessive fibrotic repair is a typical pathological feature leading to stenosis after ESD.AIM To examine the effectiveness and underlying mechanism of Kangfuxin solution(KFX)in mitigating excessive fibrotic repair of the esophagus post-ESD.METHODS Pigs received KFX at 0.74 mL/kg/d for 21 days after esophageal full circumferential ESD.Endoscopic examinations occurred on days 7 and 21 post-ESD.In vitro,recombinant transforming growth factor(TGF)-β1(5 ng/mL)induced a fibrotic microenvironment in primary esophageal fibroblasts(pEsF).After 24 hours of KFX treatment(at 1.5%,1%,and 0.5%),expression ofα-smooth muscle actin-2(ACTA2),fibronectin(FN),and type collagen I was assessed.Profibrotic signaling was analyzed,including TGF-β1,Smad2/3,and phosphor-smad2/3(p-Smad2/3).RESULTS Compared to the Control group,the groups treated with KFX and prednisolone exhibited reduced esophageal stenosis,lower weight loss rates,and improved food tolerance 21 d after ESD.After treatment,Masson staining revealed thinner and less dense collagen fibers in the submucosal layer.Additionally,the expression of fibrotic effector molecules was notably inhibited.Mechanistically,KFX downregulated the transduction levels of fibrotic functional molecules such as TGF-β1,Smad2/3,and p-Smad2/3.In vitro,pEsF exposed to TGF-β1-induced fibrotic microenvironment displayed increased fibrotic activity,which was reversed by KFX treatment,leading to reduced activation of ACTA2,FN,and collagen I.The 1.5%KFX treatment group showed decreased expression of p-Smad 2/3 in TGF-β1-activated pEsF.CONCLUSION KFX showed promise as a therapeutic option for post-full circumferential esophageal ESD strictures,potentially by suppressing fibroblast fibrotic activity through modulation of the TGF-β1/Smads signaling pathway.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
In previous papers, we proposed the important Ztransformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time. In this paper, we will use ...In previous papers, we proposed the important Ztransformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time. In this paper, we will use the Z1transformation to get the general solutions of some nonlinear partial differential equations for the first time, and use the general solutions to obtain the exact solutions of some typical definite solution problems.展开更多
In this paper, we get the N-fold Darboux transformation with multi-parameters for the coupled mKdV equations with the help of a guage transformation of the spectral problem. As an application, some new multi-soliton s...In this paper, we get the N-fold Darboux transformation with multi-parameters for the coupled mKdV equations with the help of a guage transformation of the spectral problem. As an application, some new multi-soliton solutions and complexiton solutions are obtained from choosing the appropriate seed solution. All obtained solutions and N-fold Darboux transformations are expressed using the Vandermonde-like determinants.展开更多
This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that...This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.展开更多
In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is als...In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.展开更多
The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equat...The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the N-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between N-periodic wave solutions and N-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.展开更多
Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhan...Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhancing patient prognosis.Obviously,non-participation of asymptomatic individuals in screening programs hampers early diagnosis and may adversely affect long-term outcomes for CRC patients.In this letter,we provide a comprehensive overview of the current status of early screening practices,while also thoroughly examine the dilemmas and potential solutions associated with early screening for CRC.In response to these issues,we proffer a set of recommendations directed at governmental authorities and the general public,which focus on augmenting financial investment,establishing standardized screening protocols,advancing technological capabilities,and bolstering public awareness campaigns.The importance of collaborative efforts from various stakeholders cannot be overstated in the quest to enhance early detection rates and alleviate the societal burden of CRC.展开更多
We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−...We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−1)u and V(x)≡1,it seems very difficult to apply the mountain-pass theorem to get a solution(i.e.,mountain-pass solution)to this kind of equation for all p∈(1,5),due to the difficulty of verifying the boundedness of the PalaisSmale sequence obtained by the mountain-pass theorem when p∈(1,3).In this paper,we find a new strategy to overcome this difficulty,and then get a mountain-pass solution to the equation for all p∈(1,5)and for both V(x)being constant and nonconstant.Also,we find a possibly optimal condition on V(x).展开更多
In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome...In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.展开更多
Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nano...Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.展开更多
The degradation and nonlinear interactions of a two-breather solution of the Mel’nikov equation are analyzed.By modulating the phase shift and limit method,we prove that in different regions near the non-singular bou...The degradation and nonlinear interactions of a two-breather solution of the Mel’nikov equation are analyzed.By modulating the phase shift and limit method,we prove that in different regions near the non-singular boundaries,there are four kinds of solutions with repulsive interaction or attractive interaction in addition to the two-breather solution.They are the interaction solution between soliton and breather,the two-soliton solution,and the two-breather solution with small amplitude,which all exhibit repulsive interactions;and the two-breather solution with small amplitude,which exhibits attractive interaction.Interestingly,a new breather acts as a messenger to transfer energy during the interaction between two breather solutions with small amplitude.展开更多
Background:The aim of the study was to explore a feasible method for alleviating limb ischemia-reperfusion injury(LI/RI)through the use of a high-concentration citrate solution(HC-A solution)for limb perfusion(LP).Met...Background:The aim of the study was to explore a feasible method for alleviating limb ischemia-reperfusion injury(LI/RI)through the use of a high-concentration citrate solution(HC-A solution)for limb perfusion(LP).Methods:Eighteen pigs were divided into three groups:the Sham group,LI/RI group,and HCA group.The Sham group underwent exposure of the iliac artery and vein.The LI/RI group underwent tourniquet placement and clamping of the iliac artery and vein to simulate LI/RI.The HCA group received HC-A solution LP for 30 min through the left iliac artery below the level of blood flow occlusion based on the LI/RI group.Oxidative stress markers and inflammatory response markers were compared among the three groups.Results:Compared to the LI/RI group,the HCA group showed significantly lower levels of serum creatine kinase(CK),lactate dehydrogenase(LDH),malondialdehyde(MDA),tumor necrosis factor-α(TNF-α),aspartate aminotransferase(AST),and ala-nine aminotransferase(ALT),and significantly greater activities of serum superoxide dismutase(SOD)(p<0.05).There were no significant differences in serum interleukin-6(IL-6)or in muscle MDA,SOD,TNF-α,and IL-6 between the HCA group and the LI/RI group(p>0.05).Compared to the LI/RI group,MDA,TNF-α,and IL-6 levels in the liver were significantly lower in the HCA group(p<0.05),while SOD activities were not significantly different(p>0.05).Histopathological examination revealed reduced skeletal muscle and liver damage in the HCA group compared to the LI/RI group.Conclusions:HC-A solution LP can alleviate liver damage caused by LI/RI in pigs.展开更多
In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved ...In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.展开更多
This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation b...This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.展开更多
In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)...In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.展开更多
In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div...In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R is a potential function with a local minimum and f is subcritical growth.Based on the penalization method,Nehari manifold techniques and Ljusternik-Schnirelmann category theory,we obtain the multiplicity and concentration of positive solutions to the above system.展开更多
The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were...The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were investigated using in-situ neutron diffraction and the EVPSC-TDT model.Neutron diffraction was used to quantitatively track grain-level lattice strains and diffraction intensity changes(related to mechanical twinning)in differently oriented grains of each alloy during cyclic tensile/compressive loadings.These measurements were accurately captured by the model.The stress-strain curves of Mg-1 wt%Zn and Mg-2 wt%Zn alloys show as-expected solid solution strengthening from the addition of Zn compared to pure Mg.The macroscopic yielding and hardening behaviors are explained by alternating slip and twinning modes as calculated by the model.The solid solution's influence on individual deformation modes,including basal〈a〉slip,prismatic〈a〉slip,and extension twinning,was then quantitatively assessed in terms of activity,yielding behavior,and hardening response by combining neutron diffraction results with crystal plasticity predictions.The Mg-1 wt%Zn alloy displays distinct yielding and hardening behavior due to solid solution softening of prismatic〈a〉slip.Additionally,the dependence of extension twinning,in terms of the twinning volume fraction,on Zn content exhibits opposite trends under tensile and compressive loadings.展开更多
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa...In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.展开更多
The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach...The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach to derive exact traveling wave solutions for the coupled Boussinesq equation.The solutions are articulated through soliton,trigonometric,rational,and Jacobi elliptic functions.Notably,the introduction of Jacobi elliptic function solutions for this model marks a pioneering advancement.Contour plots of the solutions obtained by assigning values to various parameters are generated and subsequently analyzed.The methodology proposed in this study offers a systematic means to tackle nonlinear partial differential equations in mathematical physics,thereby enhancing comprehension of the physical attributes and dynamics of water waves.展开更多
基金Supported by Science and Technology Department of Sichuan Province,No.2020YFS0376National Natural Science Foundation of China,No.81900599Science and Technology Program of Hospital of TCM,Southwest Medical University,No.2022-CXTD-01.
文摘BACKGROUND Esophageal stricture ranks among the most significant complications following endoscopic submucosal dissection(ESD).Excessive fibrotic repair is a typical pathological feature leading to stenosis after ESD.AIM To examine the effectiveness and underlying mechanism of Kangfuxin solution(KFX)in mitigating excessive fibrotic repair of the esophagus post-ESD.METHODS Pigs received KFX at 0.74 mL/kg/d for 21 days after esophageal full circumferential ESD.Endoscopic examinations occurred on days 7 and 21 post-ESD.In vitro,recombinant transforming growth factor(TGF)-β1(5 ng/mL)induced a fibrotic microenvironment in primary esophageal fibroblasts(pEsF).After 24 hours of KFX treatment(at 1.5%,1%,and 0.5%),expression ofα-smooth muscle actin-2(ACTA2),fibronectin(FN),and type collagen I was assessed.Profibrotic signaling was analyzed,including TGF-β1,Smad2/3,and phosphor-smad2/3(p-Smad2/3).RESULTS Compared to the Control group,the groups treated with KFX and prednisolone exhibited reduced esophageal stenosis,lower weight loss rates,and improved food tolerance 21 d after ESD.After treatment,Masson staining revealed thinner and less dense collagen fibers in the submucosal layer.Additionally,the expression of fibrotic effector molecules was notably inhibited.Mechanistically,KFX downregulated the transduction levels of fibrotic functional molecules such as TGF-β1,Smad2/3,and p-Smad2/3.In vitro,pEsF exposed to TGF-β1-induced fibrotic microenvironment displayed increased fibrotic activity,which was reversed by KFX treatment,leading to reduced activation of ACTA2,FN,and collagen I.The 1.5%KFX treatment group showed decreased expression of p-Smad 2/3 in TGF-β1-activated pEsF.CONCLUSION KFX showed promise as a therapeutic option for post-full circumferential esophageal ESD strictures,potentially by suppressing fibroblast fibrotic activity through modulation of the TGF-β1/Smads signaling pathway.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
文摘In previous papers, we proposed the important Ztransformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time. In this paper, we will use the Z1transformation to get the general solutions of some nonlinear partial differential equations for the first time, and use the general solutions to obtain the exact solutions of some typical definite solution problems.
文摘In this paper, we get the N-fold Darboux transformation with multi-parameters for the coupled mKdV equations with the help of a guage transformation of the spectral problem. As an application, some new multi-soliton solutions and complexiton solutions are obtained from choosing the appropriate seed solution. All obtained solutions and N-fold Darboux transformations are expressed using the Vandermonde-like determinants.
文摘This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.
基金Supported by the National Natural Science Foundation of China(12171247)。
文摘In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12101572 and 12371256)2024 Shanxi Province Graduate Innovation Project (Grant No. 2024KY615)the Fundamental Research Program of Shanxi Province of China (Grant No. 202403021211002)。
文摘The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the N-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between N-periodic wave solutions and N-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.
文摘Colorectal cancer(CRC)is a prevalent malignancy worldwide,posing a significant public health concern.Mounting evidence has confirmed that timely early screening facilitates the detection of incipient CRC,thereby enhancing patient prognosis.Obviously,non-participation of asymptomatic individuals in screening programs hampers early diagnosis and may adversely affect long-term outcomes for CRC patients.In this letter,we provide a comprehensive overview of the current status of early screening practices,while also thoroughly examine the dilemmas and potential solutions associated with early screening for CRC.In response to these issues,we proffer a set of recommendations directed at governmental authorities and the general public,which focus on augmenting financial investment,establishing standardized screening protocols,advancing technological capabilities,and bolstering public awareness campaigns.The importance of collaborative efforts from various stakeholders cannot be overstated in the quest to enhance early detection rates and alleviate the societal burden of CRC.
基金supported by the NSFC(11931012,11871387,12371118)。
文摘We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−1)u and V(x)≡1,it seems very difficult to apply the mountain-pass theorem to get a solution(i.e.,mountain-pass solution)to this kind of equation for all p∈(1,5),due to the difficulty of verifying the boundedness of the PalaisSmale sequence obtained by the mountain-pass theorem when p∈(1,3).In this paper,we find a new strategy to overcome this difficulty,and then get a mountain-pass solution to the equation for all p∈(1,5)and for both V(x)being constant and nonconstant.Also,we find a possibly optimal condition on V(x).
基金supported by the NSFC(11301297)the Hubei Provincial Natural Science Foundation of China(2024AFB730)+3 种基金the Yichang City Natural Science Foundation(A-24-3-008)the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(NAA2024ORG003)Gu's research was supported by the Zhejiang Provincial Natural Science Foundation(LQ21A010014)the NFSC(12101577).
文摘In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.
基金supported by Scientific Research Projects Department of Istanbul Technical University.Project Number:MGA-2018-41546.Grant receiver:E.T.
文摘Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52171251 and U21062251)Program of Science and Technology Innovation of Dalian(Grant No.2022JJ12GX036).
文摘The degradation and nonlinear interactions of a two-breather solution of the Mel’nikov equation are analyzed.By modulating the phase shift and limit method,we prove that in different regions near the non-singular boundaries,there are four kinds of solutions with repulsive interaction or attractive interaction in addition to the two-breather solution.They are the interaction solution between soliton and breather,the two-soliton solution,and the two-breather solution with small amplitude,which all exhibit repulsive interactions;and the two-breather solution with small amplitude,which exhibits attractive interaction.Interestingly,a new breather acts as a messenger to transfer energy during the interaction between two breather solutions with small amplitude.
基金Natural Science Foundation of Fujian Province,Grant/Award Number:2021J011262 and 2022J011095Youth Independent Innovation and Incubation Special Project,Grant/Award Number:2022QC07The project of 900th Hospital,Grant/Award Number:2021MS02 and 2023GK01。
文摘Background:The aim of the study was to explore a feasible method for alleviating limb ischemia-reperfusion injury(LI/RI)through the use of a high-concentration citrate solution(HC-A solution)for limb perfusion(LP).Methods:Eighteen pigs were divided into three groups:the Sham group,LI/RI group,and HCA group.The Sham group underwent exposure of the iliac artery and vein.The LI/RI group underwent tourniquet placement and clamping of the iliac artery and vein to simulate LI/RI.The HCA group received HC-A solution LP for 30 min through the left iliac artery below the level of blood flow occlusion based on the LI/RI group.Oxidative stress markers and inflammatory response markers were compared among the three groups.Results:Compared to the LI/RI group,the HCA group showed significantly lower levels of serum creatine kinase(CK),lactate dehydrogenase(LDH),malondialdehyde(MDA),tumor necrosis factor-α(TNF-α),aspartate aminotransferase(AST),and ala-nine aminotransferase(ALT),and significantly greater activities of serum superoxide dismutase(SOD)(p<0.05).There were no significant differences in serum interleukin-6(IL-6)or in muscle MDA,SOD,TNF-α,and IL-6 between the HCA group and the LI/RI group(p>0.05).Compared to the LI/RI group,MDA,TNF-α,and IL-6 levels in the liver were significantly lower in the HCA group(p<0.05),while SOD activities were not significantly different(p>0.05).Histopathological examination revealed reduced skeletal muscle and liver damage in the HCA group compared to the LI/RI group.Conclusions:HC-A solution LP can alleviate liver damage caused by LI/RI in pigs.
文摘In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.
基金Supported by Research Start-up Fund of Jianghan University(06050001).
文摘This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.
基金supported by the Natural Science Foundation of Sichuan(No.2023NSFSC0073)。
文摘In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.
基金supported by the Natural Science Foundation of Gansu Province(No.24JRRP001)。
文摘In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R is a potential function with a local minimum and f is subcritical growth.Based on the penalization method,Nehari manifold techniques and Ljusternik-Schnirelmann category theory,we obtain the multiplicity and concentration of positive solutions to the above system.
基金supported by the National Research Foundation grant funded by the Korean government(No,2023R1A2C2007190,RS-2024-00398068)partially funded by the Natural Science Foundation of Shandong Province,China(No.ZR2022QE206).
文摘The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were investigated using in-situ neutron diffraction and the EVPSC-TDT model.Neutron diffraction was used to quantitatively track grain-level lattice strains and diffraction intensity changes(related to mechanical twinning)in differently oriented grains of each alloy during cyclic tensile/compressive loadings.These measurements were accurately captured by the model.The stress-strain curves of Mg-1 wt%Zn and Mg-2 wt%Zn alloys show as-expected solid solution strengthening from the addition of Zn compared to pure Mg.The macroscopic yielding and hardening behaviors are explained by alternating slip and twinning modes as calculated by the model.The solid solution's influence on individual deformation modes,including basal〈a〉slip,prismatic〈a〉slip,and extension twinning,was then quantitatively assessed in terms of activity,yielding behavior,and hardening response by combining neutron diffraction results with crystal plasticity predictions.The Mg-1 wt%Zn alloy displays distinct yielding and hardening behavior due to solid solution softening of prismatic〈a〉slip.Additionally,the dependence of extension twinning,in terms of the twinning volume fraction,on Zn content exhibits opposite trends under tensile and compressive loadings.
文摘In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach to derive exact traveling wave solutions for the coupled Boussinesq equation.The solutions are articulated through soliton,trigonometric,rational,and Jacobi elliptic functions.Notably,the introduction of Jacobi elliptic function solutions for this model marks a pioneering advancement.Contour plots of the solutions obtained by assigning values to various parameters are generated and subsequently analyzed.The methodology proposed in this study offers a systematic means to tackle nonlinear partial differential equations in mathematical physics,thereby enhancing comprehension of the physical attributes and dynamics of water waves.
