Subharmonic solutions of Hamiltonian systems and the Maslov-type index theory

This paper deals with the subharmonic solutions of Hamiltonian systems

(H)     

Multiple periodic solutions for nonautonomous Hamiltonian systems

In this paper, by the use of minimax method, we obtain some existence and multiplicity theorems for periodic solutions of nonautonomous Hamiltonian systems with bounded nonlinearity of the type:¶ J [(x)\dot] + ?H(t, x) + e(t) = 0. J \dot x + \nabla H(t, x) + e(t) = 0.     

Non-collision periodic solutions for singular Hamiltonian systems

We study the existence of classical (non-collision) T-periodic solutions of the Hamiltonian system where and is a T-periodic function in t which has a singularity at like Under suitable conditions on H, we prove that if then (HS) possesses at least one non-collision solution and if then the generalized solution of (HS) obtained in [5] has at most one time of collision in its period.     

Morse theory for periodic solutions of hamiltonian systems and the maslov index

In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over π₂ (M). The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an index theorem for the Fredholm operator which plays a central role in Floer homology. The index formula involves the Maslov index of nondegenerate contractible periodic solutions. This Maslov index plays the same role as the Morse index of a nondegenerate critical point does in finite dimensional Morse theory. We shall use this connection between Floer homology and Maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every 1-periodic solution has at least one Floquet multiplier which is not equal to 1.     

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.     

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.     

碰撞Hamiltonian系统的无穷小周期解

本文通过适当的坐标变换将碰撞振子的相平面转变为全平面,应用Poincaré-Birkhoff扭转定理,证明了在原点附近超线性碰撞振子的无穷多弹性周期解的存在性,从而推广了已有的结果.     

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.     

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.     

二阶非自治Hamilton 系统周期解的新结果

研究了二阶非自治Hamilton系统（t）-B（t）x（t）＋▽H（t,x（t））=0,在局部超二次条件下周期解的存在性问题,利用山路定理和局部环绕定理得到了新的存在性定理,改进了已有结果.     

New periodic solutions for a class of singular Hamiltonian systems

In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with (PSC)c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials.     

A twist condition and periodic solutions of Hamiltonian systems

In this paper, we investigate existence of nontrivial periodic solutions to the Hamiltonian system

(HS)     

Sturm intersection theory for periodic Jacobi matrices and linear Hamiltonian systems

Sturm–Liouville oscillation theory for periodic Jacobi operators with matrix entries is discussed and illustrated. The proof simplifies and clarifies the use of intersection theory of Bott, Maslov and Conley–Zehnder. It is shown that the eigenvalue problem for linear Hamiltonian systems can be dealt with by the same approach.     

Existence of periodic solutions of sublinear Hamiltonian systems

The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need additional conditions to ensure the existence of periodic bouncing solutions.