The existence of solutions for the Dirichlet problem associated to bounded perturbations of positively-(p; q)-homogeneous Hamiltonian systems is considered both in nonresonant and resonant situations. In order to deal with the resonant case, the existence of a couple of lower and upper solutions is assumed. Both the well-ordered and the non-well-ordered cases are analysed. The proof is based on phase-plane analysis and topological degree theory.

On the Dirichlet problem associated with bounded perturbations of positively-(p, q)- homogeneous Hamiltonian systems

Fonda, Alessandro;Klun, Giuliano;Obersnel, Franco;Sfecci, Andrea
2022-01-01

Abstract

The existence of solutions for the Dirichlet problem associated to bounded perturbations of positively-(p; q)-homogeneous Hamiltonian systems is considered both in nonresonant and resonant situations. In order to deal with the resonant case, the existence of a couple of lower and upper solutions is assumed. Both the well-ordered and the non-well-ordered cases are analysed. The proof is based on phase-plane analysis and topological degree theory.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3037847
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