Aplicações do Teorema do Passo da Montanha a problemas elípticos não lineares

Abstract

One of the methods for solving differential equations is the variational method, which basically involves associating the problem with an appropriate differentiable functional, so that the critical points of this functional are the solutions we desire. For the study of this work, we used one of the theorems from critical point theory, called the Mountain Pass Theorem developed by Ambrosetti and Rabinowitz, to find positive solutions for a class of nonlinear elliptic problems with and without the Ambrosetti-Rabinowitz condition. We also show a result of non-existence of positive solutions. The study covers cases where f(x, s) is asymptotically linear with respect to s at infinity and also cases where f(x, s) is subcritical and superlinear at infinity