Existence and nonexistence of positive solutions to the fractional equation Δ^α/2 u = –u^γ in bounded domains

Abstract

Abstract. This paper deals with the question of the existence of a positive solution to the boundary value problem involving the fractional Laplacian, for γ > 1, where δ(x) denotes the Euclidean distance from x to the boundary ∂D. We distinguish two cases of nonnegative data f : trivial and nontrivial.