Existência de múltiplas soluções para classes de problemas elípticos com função peso mudando de sinal em domínios ilimitados

Abstract

The aim of this work is to give some suficient conditions for the existence and multiplicity of the solutions for a class of elliptic problems with sign-changing weight function in unbounded domains, using for this variational techniques. Specifically, in the semilinear case we use the minimization arguments on the Nehari manifold. For the quasilinear case, as in the scalar case as in the system, we use the minimization arguments and a variant of the mountain pass Theorem without the Palais-Smale condition.