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

Chungen Liu; Xiaofei Zhang

doi:10.3934/dcds.2017064

Article Contents

2017, Volume 37, Issue 3: 1559-1574. Doi: 10.3934/dcds.2017064

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

Chungen Liu^, and
Xiaofei Zhang

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

* Corresponding author: Chungen Liu
* Corresponding author: Chungen Liu

Received: May 31, 2016

Revised: September 30, 2016

Published: May 2017

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

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Abstract

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.

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Mathematics Subject Classification: 35F60, 53D12, 58E05.

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