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.
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