一阶带线性部分Hamilton系统的周期解

Abstract

Abstract:

In this paper, we consider the existence and multiplicity of periodic solutions for the first order Hamiltonian system with linear part by using the minimax methods. When the linear part is definite, under weaker condition than known ones, by using the generalized Mountain Pass Lemma, we obtain the system has at least one nonconstant periodic solution. Moreover, when the potential is even, by using the Fountain Theorem, we obtain that system has infinitely many nonconstant periodic solutions.

Key words: Hamiltonian system, Periodic solution, Critical point, Generalized Mountain Pass Lemma, Fountain Theorem

CLC Number:

37J45

ZHANG Xing-Yong. Periodic Solutions for the First Order Hamiltonian System with Linear Part[J].Acta mathematica scientia,Series A, 2013, 33(5): 894-905.

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Periodic Solutions for the First Order Hamiltonian System with Linear Part

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