Existência de soluções via métodos variacionais para uma classe de problemas quasilineares com expoentes variáveis.

Abstract

In this thesis we establish existence and multiplicity results for solutions to some classes of problems on RN involving the p(x)-Laplacian operator. In the first part, we consider classes of problems dealing with nonlinearities possessing critical growth. Ultimately, we consider a class of problems with a nonlinearity possessing a subcritical growth. In this latter case, we searched for multi-bump solutions. Among the tools we used are Mountain Pass Theorem, Concentration-Compactness Principle, Lion’s Lemma, Ekeland’s Variational Principle and Penalization Method.