Sur une classe de problèmes elliptiques non locaux et non-linéaires avec terme singulier

Abstract

In this thesis, we are interested in studying non-local semi linear elliptic problems with Dirichlet or Dirichlet-Neumann external boundary conditions. Our objective is to generalize the same type of existence and multiplicity results, known in the case of the Laplacian, in the case of the fractional Laplacian.