Nonexistence results for a class of fractional elliptic boundary value problems

In this paper we study a class of fractional elliptic problems of the form (− )su = f (x,u) in Ω, u =0 in RN \ Ω, where s ∈ (0, 1). We prove nonexistence of positive solutions when Ω is star-shaped and f is supercritical. We also derive a nonexistence result for subcritical f in some unbounded domains. The argument relies on the method of moving spheres applied to a reformulated problem using the Caffarelli–Silvestre extension (Caffarelli and Silvestre (2007) [11]) of a solution of the above problem. © 2012 Elsevier Inc. All rights reserved