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Servadei, R. and Valdinoci, E. (2012) Mountain Pass Solutions for Non-Local Elliptic Operators. Journal of Mathematical Analysis & Applications, 389, 887-898.
https://doi.org/10.1016/j.jmaa.2011.12.032

has been cited by the following article:

• TITLE: Existence and Uniqueness of Solution to Semilinear Fractional Elliptic Equation

  AUTHORS: Shangjian Liu

  KEYWORDS: Sobolev Embedding Theorem, Stampacchia’s Theorem, Existence, Uniquness

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.1, January 25, 2019

  ABSTRACT: In this work, we study the following problem. , where is the fractional Laplacian and Ωis a bounded domain in RNwith Lipschitz boundary. g: R→Ris an increasing locally Lipschitz continuous function. and f∈Lm(Ω), . We use Stampacchia’s theorem to study existence of the solution u, and we prove the uniqueness of u by contradiction.