The author proves a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition.
In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T...In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T 〉 0; moreover, such a solution has T as its minimal period.展开更多
We study some monotonicity and iteration inequality of the Maslov-type index i-1of linear Hamiltonian systems.As an application we prove the existence of symmetric periodic solutions with prescribed minimal period for...We study some monotonicity and iteration inequality of the Maslov-type index i-1of linear Hamiltonian systems.As an application we prove the existence of symmetric periodic solutions with prescribed minimal period for first order nonlinear autonomous Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity.This result gives a positive answer to Rabinowitz’s minimal period conjecture in this case without strictly convex assumption.We also give a different proof of the existence of symmetric periodic solutions with prescribed minimal period for classical Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity which was proved by Fei,Kim and Wang in 2001.展开更多
Solutions of minimal period for the Hamiltonian system =JH′(x) has been proven under the conditionas H″(x) -1 →0 as |x|→∞ and H(x) is of higher order than 2 in the neighborhood of the origin; In this paper, w...Solutions of minimal period for the Hamiltonian system =JH′(x) has been proven under the conditionas H″(x) -1 →0 as |x|→∞ and H(x) is of higher order than 2 in the neighborhood of the origin; In this paper, we extend the result to the problem J=H^′(x)+Qx with Q symmetric and H^ (x) satisfying the same assumption.展开更多
With the aid of P-index iteration theory,we consider the minimal period estimates on P-symmetric periodic solutions of nonlinear P-symmetric Hamiltonian systems with mild superquadratic growth.
The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the...The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the variational methods, an estimate on the minimal periodof the corresponding nonconstant periodic solution of the above-mentioned system is obtained.展开更多
文摘The author proves a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition.
基金supported by the 973 Project of Science and Technology
文摘In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T 〉 0; moreover, such a solution has T as its minimal period.
基金supported by National Natural Science Foundation of China (Grant Nos. 10801078,11171341 and 11271200)
文摘We study some monotonicity and iteration inequality of the Maslov-type index i-1of linear Hamiltonian systems.As an application we prove the existence of symmetric periodic solutions with prescribed minimal period for first order nonlinear autonomous Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity.This result gives a positive answer to Rabinowitz’s minimal period conjecture in this case without strictly convex assumption.We also give a different proof of the existence of symmetric periodic solutions with prescribed minimal period for classical Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity which was proved by Fei,Kim and Wang in 2001.
文摘Solutions of minimal period for the Hamiltonian system =JH′(x) has been proven under the conditionas H″(x) -1 →0 as |x|→∞ and H(x) is of higher order than 2 in the neighborhood of the origin; In this paper, we extend the result to the problem J=H^′(x)+Qx with Q symmetric and H^ (x) satisfying the same assumption.
基金The first author was supported by the Youth Fund Programs of the Science and Technology Department in Shanxi(Grant No.201901D211430)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2019L0766)+3 种基金the Doctoral Scientific Research Foundation of Shanxi Datong UniversityThe second author was partially supported by the National Natural Science Foundation of China(Grant No.11790271)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020A1515011019)the Innovation and Development Project of Guangzhou University.
文摘With the aid of P-index iteration theory,we consider the minimal period estimates on P-symmetric periodic solutions of nonlinear P-symmetric Hamiltonian systems with mild superquadratic growth.
文摘The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the variational methods, an estimate on the minimal periodof the corresponding nonconstant periodic solution of the above-mentioned system is obtained.
基金Supported by the Youth Fund Programs of the Science and Technology Department in Shanxi(201901D211430)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2019L0766)+3 种基金the Doctoral Scientific Research Foundation of Shanxi Datong Universitythe NSF of China(11790271)Guangdong Basic and Applied basic Research Foundation(2020A1515011019)Innovation and Development Project of Guangzhou University。
