Existence of positive solutions to elliptic problems involving the fractional Laplacian

This paper focuses on the following elliptic problem involving a fractional Laplacian: (-Δ)αu+V(x)u=f(u) in RN, where N≥2 , α∈(0,1) , (-Δ)α stands for the fractional Laplacian. Using some variational methods, we obtain the existence of positive solutions without compactness conditions.