Journal of Applied Mathematics
Volume 2013 (2013), Article ID 521059, 5 pages
http://dx.doi.org/10.1155/2013/521059
Research Article

Multiple Solutions for Generalized Asymptotical Linear Hamiltonian Systems Satisfying Bolza Boundary Conditions

Yuan Shan1,2 and Baoqing Liu1

1School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210023, China
2Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China

Received 20 December 2012; Accepted 28 February 2013

Academic Editor: Jinde Cao

Copyright © 2013 Yuan Shan and Baoqing Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Bolza boundary conditions. We classify the linear Hamiltonian systems by the index theory and obtain the existence and multiplicity of solutions for the Hamiltonian systems, based on an application of the classical symmetric mountain pass lemma.