Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Gabriele Bonanno

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

bonanno@unime.it

Keywords

  • Second order Hamiltonian systems
  • periodic solutions
  • critical points

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Suggested citation

G. Bonanno, R. Livrea. “Existence and Multiplicity of Periodic Solutions for Second Order Hamiltonian Systems Depending on a Parameter.” Journal of Convex Analysis 20 (2013), No. 4, 1075–1094. https://doi.org/10.68381/jca20058

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.