Problemas no lineales de tipo Ambrosetti-Prodi : Un problema de tipo Ambrosetti-Prodi con condición de frontera Dirichlet homogénea con el p-Laplaciano.

Abstract

In this work we want to determine the existence of at least one weak solution of an Ambrosetti-Prodi problem with homogeneous Dirichlet boundary condition involving p-Laplacian operator. For that purpose, we begin proposing hypothesis on the problem in order to study it under variational techniques. We show that these hypotheses imply a boundness condition very useful to study the functional associated to the problem. We are going to prove that the hypothesis also imply the Ambrosetti-Prodi conditions and we end showing the existence of a weak solution being this a minimum point for the functional associated to the problem.