Multiple periodic solutions for Hamiltonian systems with not coercive potential

doi:10.1016/j.jmaa.2009.09.025

Journal of Mathematical Analysis and Applications

Volume 363, Issue 2, 15 March 2010, Pages 627-638

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Abstract

Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems.

Keywords

Multiple solutions

Infinitely many solutions

Hamiltonian systems

Nonlinear differential problems

Critical points