The existence of solutions for the Dirichlet problem associated with bounded perturbations of positively-(p, q)-homogeneous Hamiltonian systems is considered both in nonresonant and resonant situations. 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. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - 24:4(2022). [10.1007/s11784-022-00980-7]
On the Dirichlet problem associated with bounded perturbations of positively-(p, q)- homogeneous Hamiltonian systems
Klun, Giuliano;Sfecci, Andrea
2022-01-01
Abstract
The existence of solutions for the Dirichlet problem associated with bounded perturbations of positively-(p, q)-homogeneous Hamiltonian systems is considered both in nonresonant and resonant situations. 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.| File | Dimensione | Formato | |
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