Existence and multiplicity results for the fractional Laplacian in   bounded domains
  In this paper, first we study existence results for a linearly perturbed elliptic problem driven by the fractional Laplacian. Then, we show a multiplicity result when the perturbation parameter is close to the eigenvalues. This latter result is obtained by exploiting the topological structure of the sublevels of the associated functional, which permits to apply a critical point theorem of mixed nature due to Marino and Saccon. 
Dimitri Mugnai and Dayana Pagliardini
math.AP