Nanjing Normal University, Department of Mathematics, 210046 Nanjing, Jiangsu, China
Abstract:
This paper consider the multiple solutions for even Hamiltonian systems satisfying Sturm-Liouville boundary conditions. The gradient of Hamiltonian function is generalized asymptotically linear. The solutions obtained are shown to coincide with the critical points of a dual functional. Thanks to the index theory for linear Hamiltonian systems by Dong (2010) 1], we find critical points of this dual functional by verifying the assumptions of a lemma about multiple critical points given by Chang (1993) 2].