Bifurcation and multiplicity results for critical nonlocal fractional Laplacian problems

In this paper we consider a critical nonlocal problem and we prove a multiplicity and bifurcation result for this, using a classical theorem in critical points theory. Precisely, we show that in a suitable left neighborhood of any eigenvalue of the operator which drives the equation the number of nontrivial solutions for the problem under consideration is at least twice the multiplicity of the eigenvalue. Hence, we extend a famous result got by Cerami, Fortunato and Struwe for classical elliptic equations, to the case of nonlocal fractional operators.