Existência e multiplicidade de soluções não negativas para uma classe de problemas elípticos

Abstract

In this work, we study the existence and multiplicity of non-negative solutions for some elliptic problems in a bounded domain. We deal with linear, asymptotically linear and superlinear cases. The tools used to guarantee the existence of such solutions were the Variational Methods, more specifically, the Mountain Pass Theorem and the Ekeland’s Variational Principle. To study the signal of the solutions we use the maximum principle.