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.

引用

页数：29

共 33 条

[1] Adams A., 2003, SOBOLEV SPACES
[2] Alves C.O., PREPRINT
[3] A multiplicity result for a nonlinear fractional Schrodinger equation in RN without the Ambrosetti-Rabinowitz condition
Alves, Claudianor O.
Ambrosio, Vincenzo
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 466 (01) : 498 - 522
[4] Alves CO, 2016, CALC VAR PARTIAL DIF, V55, DOI 10.1007/s00526-016-0983-x
[5] Existence of least energy nodal solution for a Schrodinger-Poisson system in bounded domains
Alves, Claudianor O.
Souto, Marco A. S.
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2014, 65 (06): : 1153 - 1166
[6] Multiplicity of solutions for a class of elliptic problem in R2 with Neumann conditions
Alves, CO
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 219 (01) : 20 - 39
[7] Sign-changing solutions for a class of Schrodinger equations with vanishing potentials
Ambrosio, Vincenzo
Isernia, Teresa
[J]. RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2018, 29 (01) : 127 - 152
[8] [Anonymous], 2004, Abstr Appl Anal, DOI DOI 10.1155/S1085337504310018
[9] Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions
Barrios, Begona
Medina, Maria
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2020, 150 (01) : 475 - 495
[10] Partial symmetry of least energy nodal solutions to some variational problems
Bartsch, T
Weth, T
Willew, M
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 2005, 96 (1): : 1 - 18

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