The existence of periodic solution for infinite dimensional Hamiltonian systems

TL;DR

This paper proves the existence of periodic solutions in infinite dimensional Hamiltonian systems using saddle point reduction, topological degree, and index methods.

Contribution

It introduces a novel approach combining saddle point reduction, topology degree, and index theory to establish periodic solutions in infinite dimensional Hamiltonian systems.

Findings

Existence of periodic solutions proven for a class of infinite dimensional Hamiltonian systems.

Application of saddle point reduction in infinite-dimensional dynamical systems.

Use of topological degree and index theory to demonstrate solution existence.

Abstract

In this paper, we will consider a kind of infinite dimensional Hamiltonian system(HS), by the method of saddle point reduction, topology degree and the index, we will get the existence of periodic solution for (HS).