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Journal of Convex Analysis 20 (2013), No. 4, 1075--1094
Copyright Heldermann Verlag 2013

Existence and Multiplicity of Periodic Solutions for Second Order Hamiltonian Systems Depending on a Parameter

Gabriele Bonanno
Dept. of Civil, Information Technology, Construction, Environmental Engineering, and Applied Mathematics, University of Messina, 98166 Messina, Italy

Roberto Livrea
Department DICEAM, University of Reggio, 89100 Reggio Calabria, Italy

The existence of at least one nontrivial periodic solution for a class of second order Hamiltonian systems depending on a parameter is obtained, under an algebraic condition on the nonlinearity G and without requiring any asymptotic behavior neither at zero nor at infinity. The existence is still deduced in the particular case when G is subquadratic at zero. Finally, two multiplicity results are proved if G, in addition, is required to fulfill some different Ambrosetti-Rabinowitz type superquadratic conditions at infinity. The approach is fully variational.

Keywords: Second order Hamiltonian systems, periodic solutions, critical points.

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