Problemas elípticos não lineares de quarta ordem e aplicações a sistemas hamiltonianos

Abstract

In this thesis, the existence and multiplicity of solutions are demonstrated for fourth order nonlinear elliptic problems, with and without parameter, defined in a bounded domain Ω ⊂ R N , with N ≥ 2. These problems are based on Orlicz spaces and can be associated with Hamiltonian systems when the inversion reduction method is applied to them. It is relevant to note that, for dimensions N ≥ 3, the analysis is conducted in reflexive spaces, unlike in dimension two where the base space lacks reflexivity.