一类二阶Hamiltonian系统的无穷多周期解

裴瑞昌,李海合

(天水师范学院数学与统计科学学院,甘肃天水 741001)

一类二阶Hamiltonian系统的无穷多周期解

裴瑞昌,李海合

(天水师范学院数学与统计科学学院,甘肃天水 741001)

研究一类超线性二阶Hamiltonian系统,且非线性项是奇的,不需要假设Ambrosetti-Rabinowitz的超二次条件,利用对称型山路引理得到无穷多周期解存在性结果.

哈密尔顿系统;周期解;超线性;对称型山路引理

1 主要结果

2 结果证明

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Infinitely periodic solutions for a class second-order Hamiltonian systems

PEI Rui-chang,LI Hai-he

(College of Mathematical and Statistical Science,Tianshui Normal University,Tianshui741001,China)

In this paper,we consider a class superlinear second order Hamiltonian systems,where the nonlinearity is odd.Under no Ambrosetti-Rabinowitz’s super quadratic condition,infinitely periodic solutions are obtained by using symmetric version mountain pass theorem.

Hamiltonian systems,periodic solutions,superlinear,symmetric version mountain pass theorem

O175

A

1008-5513(2009)04-0690-05

2008-04-21.

国家自然科学基金(10371098).

裴瑞昌(1975-),硕士,研究方向：偏微分方程.

2000MSC:34B15,58E05