Nonlocal elliptic equations involving measures

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Lv, Guangying¹  Duan, Jinqiao²  He, Jinchun³ 

[1] Henan Univ, Inst Contemporary Math, Kaifeng 475001, Henan, Peoples R China

[2] IIT, Dept Appl Math, Chicago, IL 60616 USA

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

关键词: Nonlocal Laplacian;    Radon measure;    Marcinkiewicz spaces;    Green kernel;   

DOI  :  10.1016/j.jmaa.2015.07.003

来源: Elsevier

【 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.

【 授权许可】

Free