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
bonanno@unime.it
Roberto Livrea
Department DICEAM, University of Reggio, 89100 Reggio Calabria, Italy
roberto.livrea@unirc.it
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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