Infinitely many solutions for non-local problems with broken symmetry

被引：1

作者：

Bartolo, Rossella ^{[1
]}

De Napoli, Pablo L. ^{[2
,3
]}

Salvatore, Addolorata ^{[4
]}

机构：

[1] Politecn Bari, Dipartimento Meccan Matemat & Management, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Buenos Aires, Fac Ciencias Exactas & Nat, CONICET, IMAS, Ciudad Univ, RA-1428 Buenos Aires, DF, Argentina

[3] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Ciudad Univ, RA-1428 Buenos Aires, DF, Argentina

[4] Univ Bari Aldo Moro, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari, Italy

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2018年 / 7卷 / 03期

关键词：

Fractional Laplace operator; variational methods; perturbative method; CRITICAL-POINTS; OBSTACLE PROBLEM; BOUNDARY; EQUATIONS; MULTIPLICITY; REGULARITY;

D O I：

10.1515/anona-2016-0106

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to investigate the existence of solutions of the non-local elliptic problem {(-Delta)(s)u = vertical bar u vertical bar(p-2) u + h(x) in Omega, u = 0 on R-n \ Omega, where s is an element of (0, 1), n > 2 s, Omega is an open bounded domain of R-n with Lipschitz boundary partial derivative Omega, (-Delta)(s) is the non-local Laplacian operator, 2 < p < 2*(s) and h is an element of L-2 (Omega). This problem requires the study of the eigenvalue problem related to the fractional Laplace operator, with or without potential.

引用

页码：353 / 364

页数：12

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