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

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.