Open Access Research

Existence of homoclinic solutions for a class of second-order Hamiltonian systems with subquadratic growth

Dan Zhang

Author Affiliations

Department of Mathematics, Hunan University of Science and Engineering, Yongzhou, Hunan, 425100, People’s Republic of China

Boundary Value Problems 2012, 2012:132  doi:10.1186/1687-2770-2012-132

Published: 13 November 2012

Abstract

By properly constructing a functional and by using the critical point theory, we establish the existence of homoclinic solutions for a class of subquadratic second-order Hamiltonian systems. Our result generalizes and improves some existing ones. An example is given to show that our theorem applies, while the existing results are not applicable.

Keywords:
homoclinic solutions; critical point theory; Hamiltonian systems; nontrivial solution