Fractional elliptic problem in exterior domains with nonlocal Neumann condition

被引：16

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

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.

引用

页数：29

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