Fareh, Souraya2023-11-152023-11-152023http//localhost:8080/jspui/handle/123456789/10802The 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.enp (x)-Laplacian, fractional p-Laplacian, Palais-Smale condition, variational methods, mountain pass theorem, fountain theorem, Nehari Manifold, fibering methodThesis