Sistemas elípticos com pesos envolvendo o expoente crítico de Hardy-Sobolev

Abstract

In this work, we will study the existence and nonexistence of positive weak solutions for two classes of elliptic systems with weights. The first class will involve nonlinearities of the type positone and semipositone. We will prove a strong maximum principle, and we will obtain some properties of the first eigenfunction of the eigenvalue problem associated to our operator, and also we will prove the sub and supersolution method. The second class will involve a nonlinear perturbation. We will use the variational methods to study the subcritical and critical situations, and under certain hypotheses, we will show the existence of a second weak solution.