In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational c...In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.展开更多
By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established re...By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.展开更多
It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventual...It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.展开更多
The second-order nonlinear system with delay x ' (t) + f(x(t),x ' (t)) + g(x(t),x ' (t))psi (x(t-tau)) = p(t) being considered. Four theorems on the stability of zero solution, the boundedness of the solut...The second-order nonlinear system with delay x ' (t) + f(x(t),x ' (t)) + g(x(t),x ' (t))psi (x(t-tau)) = p(t) being considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscillation are obtained by means of the Liapunov's second method, The conclusion in the literatures are generalized.展开更多
In this paper, we study the nonlinear second-order boundary value problem of delay differential equation.. Without the assumption of the nonnegativity of f, we still obtain the existence of the positive solution.
A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ ...A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.展开更多
In this paper, we discuss the existence of positive solutions of the secondorder delay boundary value problems. By applying the fixed-point theorem in a cone, we show the existence of at least one positive solution wi...In this paper, we discuss the existence of positive solutions of the secondorder delay boundary value problems. By applying the fixed-point theorem in a cone, we show the existence of at least one positive solution with singularity and the superlinear semipositone. As an demonstrate our results. application, we also give some examples todemonstrate our results.展开更多
By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to ...By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.展开更多
In this paper, with the help of Lyapunov functional approach, sufficient conditions for the asymptotic stability of zero solution for a certain fourthorder non-linear delay differential equation are given.
The outbreak of coronavirus disease 2019(COVID-19)has aroused a global alert.To release social panic and guide future schedules,this article proposes a novel mathematical model,the Delay Differential Epidemic Analyzer...The outbreak of coronavirus disease 2019(COVID-19)has aroused a global alert.To release social panic and guide future schedules,this article proposes a novel mathematical model,the Delay Differential Epidemic Analyzer(D2EA),to analyze the dynamics of epidemic and forecast its future trends.Based on the traditional Susceptible-Exposed-Infectious-Recovered(SEIR)model,the D2EA model innovatively introduces a set of quarantine states and applies both ordinary differential equations and delay differential equations to describe the transition between two states.Potential variations of practical factors are further considered to reveal the true epidemic picture.In the experiment part,we use the D^2EA model to simulate the epidemic in Hubei Province.Fitting to the collected real data as non-linear optimization,the D^2EA model forecasts that the accumulated confirmed infected cases in Hubei Province will reach the peak at the end of February and then steady down.We also evaluate the effectiveness of the quarantine measures and schedule the date to reopen Hubei Province.展开更多
文摘In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.
文摘By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.
文摘It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.
文摘The second-order nonlinear system with delay x ' (t) + f(x(t),x ' (t)) + g(x(t),x ' (t))psi (x(t-tau)) = p(t) being considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscillation are obtained by means of the Liapunov's second method, The conclusion in the literatures are generalized.
基金the Youth Research Foundation of Jiangxi University of Finance and Economics(No.04232015)the Technological Project Foundation of Jiangxi Province (Nos.GJJ08358GJJ08359)the Educational Reform Project Foundation of Jiangxi Province (No.JXJG07436)
文摘In this paper, we study the nonlinear second-order boundary value problem of delay differential equation.. Without the assumption of the nonnegativity of f, we still obtain the existence of the positive solution.
文摘A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.
文摘In this paper, we discuss the existence of positive solutions of the secondorder delay boundary value problems. By applying the fixed-point theorem in a cone, we show the existence of at least one positive solution with singularity and the superlinear semipositone. As an demonstrate our results. application, we also give some examples todemonstrate our results.
基金supported by the National Natural Science Foundation of China(10461006)Basic Subject Foundation of Changzhou University(JS201004)
文摘By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.
基金supported by the National Natural Science Foundation of China(No.11671227)
文摘In this paper, with the help of Lyapunov functional approach, sufficient conditions for the asymptotic stability of zero solution for a certain fourthorder non-linear delay differential equation are given.
基金the National Key Research and Development Program of China(No.2018YFB1004700)the National Natural Science Foundation of China(Nos.61872238 and 61972254)+1 种基金the Shanghai Science and Technology Fund(No.17510740200)the CCF-Huawei Database System Innovation Research Plan(No.CCF-Huawei DBIR2019002A)。
文摘The outbreak of coronavirus disease 2019(COVID-19)has aroused a global alert.To release social panic and guide future schedules,this article proposes a novel mathematical model,the Delay Differential Epidemic Analyzer(D2EA),to analyze the dynamics of epidemic and forecast its future trends.Based on the traditional Susceptible-Exposed-Infectious-Recovered(SEIR)model,the D2EA model innovatively introduces a set of quarantine states and applies both ordinary differential equations and delay differential equations to describe the transition between two states.Potential variations of practical factors are further considered to reveal the true epidemic picture.In the experiment part,we use the D^2EA model to simulate the epidemic in Hubei Province.Fitting to the collected real data as non-linear optimization,the D^2EA model forecasts that the accumulated confirmed infected cases in Hubei Province will reach the peak at the end of February and then steady down.We also evaluate the effectiveness of the quarantine measures and schedule the date to reopen Hubei Province.
