Problemas no lineales de tipo Ambrosetti-Prodi: técnicas de minimax para un problema de tipo Ambrosetti-Prodi con condiciones de borde Dirichlet homogéneas y no linealidades con pesos indefinidos.

Abstract

In this work we integrate the knowledge acquired throughout the Mathe- matics career, especially those referring to partial differential equations, functional analysis, and above all; the ability to investigate and solve a new problem starting from the aforementioned bases. In particular, in this work we seek a solution to a nonlinear analysis problem (elliptic se- milinear equation, which is a nonlinear generalization of a linear elliptic partial differential equation) of the Ambrosetti-Prodi type with homoge- neous Dirichlet boundary conditions and not linearities with undefined weights. Throughout the work we will explain how we found the solutions to our problem and we will expand the information on the variational methods used to find the solutions, which were: 1. Direct methos of the Calculus of variations. 2. Minimax method.