Sobre uma classe de problemas em Espaços de Orlicz-Sobolev envolvendo crescimento crítico exponencial

Abstract

This thesis addresses the existence of solutions for a class of nonlinear elliptic problems defined in Orlicz-Sobolev spaces, with emphasis on nonlinearities involving critical exponential growth. Initially, fundamental results concerning these spaces are established, serving as the foundation for the subsequent analysis. Then, by employing

variational methods and refined techniques, the existence of positive solutions is de- monstrated for semipositone problems involving the Φ-Laplacian operator, overcoming

difficulties related to the operator’s lack of homogeneity and the exponential growth of the nonlinearity. Finally, we establish the existence of a least energy nodal solution with exactly two nodal domains, extending existing results in the literature by considering more general assumptions on both the operator and the nonlinearity involved.