Multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Sturm-Liouville boundary conditions

作者：Shan, Yuan^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(14): 4809-4819.

DOI：10.1016/j.na.2011.04.053

• Even Hamiltonian system
• Sturm-Liouville boundary conditions
• Multiple solutions
• Critical point
• Index theory
• Relative Morse index
• mu-index
• Dual variational principle

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].

• 出版日期2011-10
• 单位南京师范大学