一類二階Hamiltonian系統的無窮多周期解

裴瑞昌,李海合

(天水師范學院數學與統計科學學院,甘肅天水 741001)

一類二階Hamiltonian系統的無窮多周期解

裴瑞昌,李海合

(天水師范學院數學與統計科學學院,甘肅天水 741001)

研究一類超線性二階Hamiltonian系統,且非線性項是奇的,不需要假設Ambrosetti-Rabinowitz的超二次條件,利用對稱型山路引理得到無窮多周期解存在性結果.

哈密爾頓系統;周期解;超線性;對稱型山路引理

1 主要結果

2 結果證明

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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.

國家自然科學基金(10371098).

裴瑞昌(1975-),碩士,研究方向：偏微分方程.

2000MSC:34B15,58E05