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

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].