Nonlocal elliptic equations involving measures

[摘要] In this article, we study the existence of solution for the problem (-Delta)(alpha)u = lambda f(u) + nu in Omega, u equivalent to 0 in R-N\Omega, where lambda > 0 is a parameter, alpha is an element of (0,1) and nu is a Radon measure. A weak solution is obtained by using Schauder's fixed point theorem. In the case where nu is Dirac measure, the symmetry of the solution is obtained by using the moving plane method. (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Nonlocal Laplacian;Radon measure;Marcinkiewicz spaces;Green kernel