Existência de soluções para uma classe geral de operadores do tipo p&q-Laplacianos

Abstract

In this work, we will study the existence of non-trivial weak solutions for two classes of elliptic and nonlinear problems, whose growth condition on these nonlinearities is subcritical and which involve general operators of the p&q-Laplacian type. The first problem will address the existence of non-trivial weak solutions for a general class of eigenvalue problems, which was studied in [9]. In the second problem we study the existence of multiple solutions for a class of equations similar to the previous one, by adding a perturbation to the nonlinearity. The tecniques was motived by the thesys [32]. The main tools in your study are variational methods, including the classic Ekeland Variational Principle and the Mountain Pass Theorem.