裴瑞昌,李海合

(天水師范學(xué)院數(shù)學(xué)與統(tǒng)計(jì)科學(xué)學(xué)院,甘肅天水 741001)

一類二階Hamiltonian系統(tǒng)的無(wú)窮多周期解

裴瑞昌,李海合

(天水師范學(xué)院數(shù)學(xué)與統(tǒng)計(jì)科學(xué)學(xué)院,甘肅天水 741001)

研究一類超線性二階Hamiltonian系統(tǒng),且非線性項(xiàng)是奇的,不需要假設(shè)Ambrosetti-Rabinowitz的超二次條件,利用對(duì)稱型山路引理得到無(wú)窮多周期解存在性結(jié)果.

哈密爾頓系統(tǒng);周期解;超線性;對(duì)稱型山路引理

1 主要結(jié)果

2 結(jié)果證明

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[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.

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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(guó)家自然科學(xué)基金(10371098).

裴瑞昌(1975-),碩士,研究方向：偏微分方程.

2000MSC:34B15,58E05