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october 2014 Existence and multiplicity of periodic solutions for some second order Hamiltonian systems
Yiwei Ye, Chun-Lei Tang
Bull. Belg. Math. Soc. Simon Stevin 21(4): 613-633 (october 2014). DOI: 10.36045/bbms/1414091006

Abstract

In this paper, we study the existence of nontrivial periodic solutions for the second order Hamiltonian systems $ \ddot u(t)+\nabla F(t,u(t))=0$, where $F(t,x)$ is either nonquadratic or superquadratic as $|u|\mathbb{R}ightarrow \infty$. Furthermore, if $F(t,x)$ is even in $x$, we prove the existence of infinitely many periodic solutions for the general Hamiltonian systems $ \ddot u(t)+A(t)u(t)+\nabla F(t,u(t))=0$, where $A(\cdot)$ is a continuous $T$-periodic symmetric matrix. Our theorems mainly improve the recent result of Tang and Jiang [X.H. Tang, J. Jiang, Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems, Comput. Math. Appl. 59 (2010) 3646-3655].

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Yiwei Ye. Chun-Lei Tang. "Existence and multiplicity of periodic solutions for some second order Hamiltonian systems." Bull. Belg. Math. Soc. Simon Stevin 21 (4) 613 - 633, october 2014. https://doi.org/10.36045/bbms/1414091006

Information

Published: october 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1316.34046
MathSciNet: MR3271324
Digital Object Identifier: 10.36045/bbms/1414091006

Subjects:
Primary: 34A34 , 34C25 , 37J45

Keywords: Fountain Theorem , Mountain pass theorem , periodic solutions , Second-order Hamiltonian systems

Rights: Copyright © 2014 The Belgian Mathematical Society

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Vol.21 • No. 4 • october 2014
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