Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0...Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.展开更多
In this paper, a sufficient condition for the periodic solution with prescribed period for a class of superquadratic second order Hamiltonian systems x¨+Ax+ Δ F(x)=0 is obtained by using the critical point theor...In this paper, a sufficient condition for the periodic solution with prescribed period for a class of superquadratic second order Hamiltonian systems x¨+Ax+ Δ F(x)=0 is obtained by using the critical point theory, where A≠0 and is an n×n real symmetric matrix and is non definite.展开更多
研究了阻尼振动问题{(t)+g(t)(t)=▽F(t,u(t)),a.e.t∈[0,T];u(0)-u(T)=(0)-(T)=0.其中,T>0,g(t)∈L∞(0,T;R),G(t)=integral from n=0 to t g(s)ds,G(T)=0,F:[0,T]×RN→R.给出了其变分原理和2个周期解的存在性定理.即...研究了阻尼振动问题{(t)+g(t)(t)=▽F(t,u(t)),a.e.t∈[0,T];u(0)-u(T)=(0)-(T)=0.其中,T>0,g(t)∈L∞(0,T;R),G(t)=integral from n=0 to t g(s)ds,G(T)=0,F:[0,T]×RN→R.给出了其变分原理和2个周期解的存在性定理.即使在g(t)=0特殊情况下,所得结果也是新的.展开更多
<正> This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the line...<正> This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the linear Hamiltonian systems with continuous, periodic, and symmetric coefficients. Associating this index with each periodic solution, we establish the existence of muhiple periodic solutions of asymptotically linear Hamihonian systems.展开更多
The authors establish the existence of nontrival periodic solntions of the asymptotically linear Hamiltonian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by ...The authors establish the existence of nontrival periodic solntions of the asymptotically linear Hamiltonian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.展开更多
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
In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonom...In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems （H） ü＋A（t）u＋∨V（t, u）=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.展开更多
We first establish Maslov index for non-canonical Hamiltonian system by using symplectic transformation for Hamiltonian system.Then the existence of multiple periodic solutions for the non-canonical Hamiltonian system...We first establish Maslov index for non-canonical Hamiltonian system by using symplectic transformation for Hamiltonian system.Then the existence of multiple periodic solutions for the non-canonical Hamiltonian system is obtained by applying the Maslov index and Morse theory.As an application of the results,we study a class of non-autonomous differential delay equation which can be changed to non-canonical Hamiltonian system and obtain the existence of multiple periodic solutions for the equation by employing variational method.展开更多
文摘Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.
文摘In this paper, a sufficient condition for the periodic solution with prescribed period for a class of superquadratic second order Hamiltonian systems x¨+Ax+ Δ F(x)=0 is obtained by using the critical point theory, where A≠0 and is an n×n real symmetric matrix and is non definite.
基金supported by Science and Technology Plan Foundation of Guangdong Province(2006J1-C0341)Science Foundation of the Education Department of Fujian Province(JA06035)~~
文摘研究了阻尼振动问题{(t)+g(t)(t)=▽F(t,u(t)),a.e.t∈[0,T];u(0)-u(T)=(0)-(T)=0.其中,T>0,g(t)∈L∞(0,T;R),G(t)=integral from n=0 to t g(s)ds,G(T)=0,F:[0,T]×RN→R.给出了其变分原理和2个周期解的存在性定理.即使在g(t)=0特殊情况下,所得结果也是新的.
文摘<正> This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the linear Hamiltonian systems with continuous, periodic, and symmetric coefficients. Associating this index with each periodic solution, we establish the existence of muhiple periodic solutions of asymptotically linear Hamihonian systems.
文摘The authors establish the existence of nontrival periodic solntions of the asymptotically linear Hamiltonian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
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 NSFC(10471075)NSFSP(Y2003A01)NSFQN(xj0503)
文摘In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems （H） ü＋A（t）u＋∨V（t, u）=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.
基金supported by Natural Science Foundation of the Jiangsu Higher Education Institutions(Grant No.12KJB110015)
文摘We first establish Maslov index for non-canonical Hamiltonian system by using symplectic transformation for Hamiltonian system.Then the existence of multiple periodic solutions for the non-canonical Hamiltonian system is obtained by applying the Maslov index and Morse theory.As an application of the results,we study a class of non-autonomous differential delay equation which can be changed to non-canonical Hamiltonian system and obtain the existence of multiple periodic solutions for the equation by employing variational method.
