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

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

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

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

Received:2018-04-20 Online:2019-12-30 Published:2020-08-21
Contact: 1.CHEN Yu-song (1988-), male, native of Yucheng, Henan, teaching assistant of Shangqiu Institute of Technology, engages in nonlinear functional analysis; 2.CHANG He-jie (1988-), femal, native of Luohe, Henan, teaching assistan of Luohe Vocational Technology College, engages in nonlinear functional analysis.
Supported by:
Supported by the Youth Foundation of Shangqiu Institute of Technology(No.2018XKQ01)；

Abstract

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

CLC Number:

O175

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.

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

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