Elliptic problems involving the fractional Laplacian in RN

We study the existence and multiplicity of solutions for elliptic equations in RN, driven by a non-local integro-differential operator, which main prototype is the fractional Laplacian. The model under consideration, denoted by (P-lambda), depends, on a real parameter lambda and involves two superlinear nonlinearities, one of which could be critical or even supercritical. The main theorem of lambda the paper establishes the existence of three critical values of A which divide the real line in different intervals, where (P-lambda) admits no solutions, at least one nontrivial non-negative entire solution and two nontrivial non-negative entire solutions. (C) 2013 Elsevier Inc. All rights reserved.