Elliptic problems involving the fractional Laplacian in RN

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

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