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Open Access Research

Existence of subharmonic solutions for non-quadratic second-order Hamiltonian systems

Xingyong Zhang1* and Xianhua Tang2

Author Affiliations

1 Department of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan, 650500, P.R. China

2 School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan, 410083, P.R. China

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Boundary Value Problems 2013, 2013:139  doi:10.1186/1687-2770-2013-139

Published: 30 May 2013

Abstract

In this paper, some existence theorems are obtained for subharmonic solutions of second-order Hamiltonian systems with linear part under non-quadratic conditions. The approach is the minimax principle. We consider some new cases and obtain some new existence results.

MSC: 34C25, 58E50, 70H05.

Keywords:
second-order Hamiltonian systems; subharmonic solution; critical point; linking theorem