American Institute of Mathematical Sciences

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

Periodic solutions of Hamiltonian systems with anisotropic growth

 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.
Citation: Tianqing An, Zhi-Qiang Wang. Periodic solutions of Hamiltonian systems with anisotropic growth. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1069-1082. doi: 10.3934/cpaa.2010.9.1069
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