Study of some fractional elliptic problems

Abstract

The work presented in this thesis is devoted to the study of the existence and multiplicity positive non-trivial solutions of a fractional p-Laplacian problem. The results are obtained using some variational techniques. The first result is that of the existence of two non-trivial positive solutions, using the Nehari manifold and the fibering method, in the critical and subcritical cases. The second result contains the existence of three distinct solutions, only in the critical case, using Ekeland’s variational principle, under different assumptions.