Fractional elliptic problem in exterior domains with nonlocal Neumann condition

被引：14
|
作者：
Alves, Claudianor O. [1 ,2 ]
Torres Ledesma, Cesar E. [1 ,2 ]
机构：
[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429970 Campina Grande, Paraiba, Brazil
[2] Univ Nacl Trujillo, Dept Matemat, Av Juan Pablo II S-N, Trujillo, Peru
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 195卷 / 195期
关键词：
Variational methods; Nonlinear elliptic equations; Integral representations of solutions; SCHRODINGER-EQUATION; MULTIPLE SOLUTIONS; POSITIVE SOLUTIONS; NODAL SOLUTIONS;
D O I：
10.1016/j.na.2019.111732
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the existence of solution for the following class of fractional elliptic problem {(-Delta)(s)u + u = Q(x)vertical bar u vertical bar(p-1)u in R-N \ Omega (0.1) N(s)u(x) = 0 in Omega, where s is an element of (0, 1), N > 2s, Omega subset of R-N is a bounded set with smooth boundary, (-Delta)(s) denotes the fractional Laplacian operator and N-s is the nonlocal operator that describes the Neumann boundary condition, which is given by N(s)u(x) = C-N,C-s integral(RN\Omega) u(x) - u(y)/vertical bar x - y vertical bar(N+2s) dy, x is an element of Omega. (C) 2019 Elsevier Ltd. All rights reserved.
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页数：29
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