Nonlocal elliptic equations involving measures

作者:Lv, Guangying; Duan, Jinqiao*; He, Jinchun
来源:Journal of Mathematical Analysis and Applications, 2015, 432(2): 1106-1118.
DOI:10.1016/j.jmaa.2015.07.003

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.