Existence and multiplicity of solutions for certain nonlinear elliptic problems

Abstract

The problem addressed in this thesis concerns the study of some nonlinear elliptic problems. Our approach is based on variational methods. First, we studied a critical Schrödinger- Kirchhoff type system involving the fractional p-Laplacian operator with Dirichlet boundary conditions, where we proved the existence of two weak solutions by using the Nehari manifold and the fibering method. Second, we considered a class of p(x)-Laplacian problems. By applying the mountain pass theorem and fountain theorem, respectively, the existence and multiplicity of solutions were obtained.