Minimal period estimates on P-symmetric periodic solutions of first-order mild superquadratic Hamiltonian systems

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.     

一阶次二次凸Hamilton系统的最小P-边值解

利用对偶变分原理,将一阶次二次凸Hamilton系统的P-边值解问题转化为对偶变分问题,证明对偶泛函满足最小作用原理,进而推导出非平凡P-边值解的存在性结果,最后通过比较作用泛函的临界值,给出该P-边值解的最小周期估计.     

Multiplicity results for periodic solutions with prescribed minimal periods to discrete Hamiltonian systems

By making use of minimax theory and geometrical index theory, some results on the existence and multiplicity of subharmonic solutions with prescribed minimal period to discrete Hamiltonian systems are obtained.     

Periodic solutions with prescribed minimal period for the second order Hamiltonian systems with even potentials

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.     

Computation of periodic solutions of Hamiltonian systems

This paper attempts to give a practical method to compute global periodic solutions of autonomous Hamiltonian systems of arbitrary finite order. The proposed numerical method is based on continuation of solutions branching from equlibrium points and requires no iterations. Moreover, during computation of one-parameter families of periodic orbits, their possible bifurcations are determined as well.     

Applications of Clark duality to periodic solutions with minimal period for discrete Hamiltonian systems

By making use of Clark duality, perturbation technique and dual least action principle, some results on the existence of subharmonic solutions with minimal period to second-order subquadratic discrete Hamiltonian systems are obtained.     

Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems

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.     

On the minimal periodic solutions of nonconvex superlinear Hamiltonian systems

This paper proves a multiplicity result for the minimal periodic solutions of Hamiltonian system under a superquadratic hypothesis on H weaker than the Ambrosetti-Rabinowitz-type condition. We also define a class of homogeneous functions, that are more general than the classical ones, and prove the Rabinowitz's conjecture in the case of H satisfying such new homogeneity.     

Existence of periodic solutions for Hamiltonian systems with super-linear and sign-changing nonlinearities

In this paper, we consider the existence of periodic solutions for the super quadratic second order Hamiltonian system, and primitive functions of nonlinearities are allowed to be sign-changing. By using some weaker conditions, our result extends and improves some existed results in the literature.     

Multiple periodic orbits of asymptotically linear autonomous convex Hamiltonian systems

We investigate multiple periodic solutions of convex asymptotically linear autonomous Hamiltonian systems. Our theorem generalizes a result by Mawhin and Willem.     

Existence of periodic solutions for a class of second-order discrete Hamiltonian systems

By using the variant fountain theorem, we study the existence of periodic solutions for a class of superquadratic non-autonomous second-order discrete Hamiltonian systems.     

Multiple periodic solutions for non-canonical Hamiltonian systems with application to differential delay equations

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.     

Multiple periodic solutions for Hamiltonian systems with not coercive potential

Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems.     

Rotating periodic solutions for super-linear second order Hamiltonian systems

In this paper we consider a class of super-linear second order Hamiltonian systems. We use Morse theory to obtain the existence and multiplicity of rotating periodic solutions, which might be periodic, subharmonic or quasi-periodic ones.     

一类二阶Hamiltonian系统的无穷多周期解

研究一类超线性二阶Hamiltonian系统,且非线性项是奇的,不需要假设Ambros-etti-Rabinowitz的超二次条件,利用对称型山路引理得到无穷多周期解存在性结果.     

Hamiltonian constants for several new entire solutions

Using the Hamiltonian identities and the corresponding Hamiltonian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.      

Existence of periodic solutions for second-order Hamiltonian systems with asymptotically linear conditions

We consider a class of asymptotically linear nonautonomous second-order Hamiltonian systems. Using the Saddle Point Theorem, we obtain the existence result, which extends some previously known results.     

Stability criteria for linear periodic Hamiltonian systems

In this paper, we obtain new stability criteria for linear periodic Hamiltonian systems. A Lyapunov type inequality is established. Our results improve the existing works in the literature.