# American Institute of Mathematical Sciences

March  2017, 37(3): 1559-1574. doi: 10.3934/dcds.2017064

## Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth

 School of Mathematics and LPMC, Nankai University, Tianjin 300071, China

* Corresponding author: Chungen Liu

Received  June 2016 Revised  October 2016 Published  December 2016

Fund Project: The first author is supported partially by the NSF of China (11071127,10621101), 973 Program of MOST (2011CB808002) and SRFDP.

Using a homologically link theorem in variational theory and iteration inequalities of Maslov-type index, we show the existence of a sequence of subharmonic solutions of non-autonomous Hamiltonian systems with the Hamiltonian functions satisfying some anisotropic growth conditions, i.e., the Hamiltonian functions may have simultaneously, in different components, superquadratic, subquadratic and quadratic behaviors. Moreover, we also consider the minimal period problem of some autonomous Hamiltonian systems with anisotropic growth.

Citation: Chungen Liu, Xiaofei Zhang. Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1559-1574. doi: 10.3934/dcds.2017064
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