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. © Heldermann Verlag.

Bonanno, G., Livrea, R. (2013). Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter. JOURNAL OF CONVEX ANALYSIS, 20(4), 1075-1094.

Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter

Livrea, Roberto
2013-01-01

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. © Heldermann Verlag.
http://www.heldermann.de/JCA/jcacon.htm
Bonanno, G., Livrea, R. (2013). Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter. JOURNAL OF CONVEX ANALYSIS, 20(4), 1075-1094.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/258562
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