Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth

We prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to h...

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Veröffentlicht in:Advances in nonlinear analysis 2017-07, Vol.8 (1), p.583-602
Hauptverfasser: Fonda, Alessandro, Toader, Rodica
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is carried out by the use of a generalized version of the Poincaré–Birkhoff Theorem. Different situations, including Lotka–Volterra systems, or systems with singularities, are also illustrated.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2017-0040