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.