Existence and Multiplicity of Periodic Solutions for The Non-autonomous Second-order Hamiltonian Systems

CHEN Yu-song, CHANG He-jie

doi:10.13371/j.cnki.chin.q.j.m.2019.04.005

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 4: 382 - 396

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.04.005

Existence and Multiplicity of Periodic Solutions for The Non-autonomous Second-order Hamiltonian Systems

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1. Department of Basic Education,Shangqiu Institute of Technology 2. Department of Basic Education,Luohe Vocational Technology College

Received date: 2018-04-20

Online published: 2020-08-21

Supported by

Supported by the Youth Foundation of Shangqiu Institute of Technology(No.2018XKQ01)；

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Abstract

In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.

Key words： Periodic solution; Second-order Hamiltonian system; Saddle Point Theorem; Sobolev's inequality; Wirtinger's inequality

Cite this article

CHEN Yu-song, CHANG He-jie . Existence and Multiplicity of Periodic Solutions for The Non-autonomous Second-order Hamiltonian Systems[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(4) : 382 -396 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.04.005

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