一类二阶Hamiltonian系统的无穷多周期解

2009-07-05 14:26裴瑞昌李海合
纯粹数学与应用数学 2009年4期
关键词:瑞昌天水山路

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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[2]Tang chunlei.Periodic solutions for second systems at resonance[J].Acta.Math.Sinica New series,1998, 14(4):433-440.

[3]Tang chunlei.Periodic solutions for second systems with sublinear nonlinearity[J].Proceedings of the American Society,1998,126(11):3263-3270.

[4]Xu xiangjin.Homolinic orbits for first order Hamiltonian systems possessing super-quadratic potentials[J]. Nonlinear Anal.,2002,51:197-214.

[5]Zou wenming.Infinitely many Homolinic orbits for the second order Hamiltonian systems[J].Applied Mathematics Letters,2003,16:1283-1287.

[6]Zhou H S.Existence of asymptotically linear Dirichlet problem[J].Nonlinear Anal.,2001,44:909-918.

[7]Mawhin J,Willem M.Critical Point Theory and Hamilton Systems[M].New York:Springer-verlag,1989.

[8]Rabinowitz P H.Minimax Methods in Critical Point Theory with Applications to Differitional Equations: CBMS Regional Conference Series in Math,No.65[C].Rhode Island:American Mathematical society,1986.

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

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