American Institute of Mathematical Sciences

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July  2010, 9(4): 1069-1082. doi: 10.3934/cpaa.2010.9.1069

Periodic solutions of Hamiltonian systems with anisotropic growth

Tianqing An 1, and  Zhi-Qiang Wang 2,

1. 

Department of Mathematics, Hohai University, Nanjing, 210098, China
2. 

Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, United States

Received  August 2009 Revised  February 2010 Published  April 2010

In this paper we obtain some existence and multiplicity results for periodic solutions of nonautonomous Hamiltonian systems $\dot z(t)=J\nabla H(z(t),t)$ whose Hamiltonian functions may have simultaneously, in different components, superquadratic, subquadratic and quadratic behaviors. Our results generalize some earlier work [3] of P. Felmer and [5] of P. Felmer and Z.-Q. Wang.
Keywords: growth conditions, Hamiltonian system, minimax theorems., Periodic solution.
Mathematics Subject Classification: Primary: 34C25; 58E05; Secondary: 58F0.
Citation: Tianqing An, Zhi-Qiang Wang. Periodic solutions of Hamiltonian systems with anisotropic growth. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1069-1082. doi: 10.3934/cpaa.2010.9.1069
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