Existence of solutions for a class of fractional elliptic problems on exterior domains

This work concerns with the existence of solutions for the following class of nonlocal elliptic problems {(-Delta)(s) u + u = vertical bar u vertical bar(p-2) u in Omega, u >= 0 in Omega and u not equivalent to 0, u = 0 R-N\ Omega, involving the fractional Laplacian operator (-Delta)(s) , where s is an element of (0, 1), N > 2s, Omega subset of R-N is an exterior domain with (non-empty) smooth boundary partial derivative Omega and p is an element of (2, 2(s)*). The main technical approach is based on variational and topological methods. The variational analysis that we perform in this paper dealing with exterior domains is quite general and may be suitable for other goals too. (C) 2019 Elsevier Inc. All rights reserved.