FRACTIONAL ELLIPTIC EQUATIONS WITH SIGN-CHANGING AND SINGULAR NONLINEARITY

被引：0

作者：

Goyal, Sarika ^{[1
]}

Sreenadh, Konijeti ^{[1
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, Hauz Khas, New Delhi 16, India

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年

关键词：

Non-local operator; singular nonlinearity; Nehari manifold; sign-changing weight function; BREZIS-NIRENBERG RESULT; POSITIVE SOLUTIONS; REGULARITY; EXISTENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the fractional Laplacian equation with singular nonlinearity (-Delta)(s)u = a(x)u(-q) + lambda b(x)u(p) in Omega, u > 0 in Omega, u = 0 in partial derivative Omega, where Omega is a bounded domain in R-n with smooth boundary partial derivative Omega, n > 2s, s is an element of (0, 1), lambda > 0. Using variational methods, we show existence and multiplicity of positive solutions.

引用

页数：23

共 27 条

[1]

[Anonymous], P INDIAN ACAD SCI MA

[2]

[Anonymous], ARXIV150202222V1MATH

[3]

[Anonymous], 2014, ARXIV14033149V1

[4]

Applebaum D., 2004, Notices Am. Math. Soc, V51, P1336

[5] Semilinear problems for the fractional laplacian with a singular nonlinearity [J].

Barrios, Begona ;

De Bonis, Ida ;

Medina, Maria ;

Peral, Ireneo .

OPEN MATHEMATICS, 2015, 13 :390-407

[6] A concave-convex elliptic problem involving the fractional Laplacian [J].

Braendle, C. ;

Colorado, E. ;

de Pablo, A. ;

Sanchez, U. .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (01) :39-71

[7] Positive solutions of nonlinear problems involving the square root of the Laplacian [J].

Cabre, Xavier ;

Tan, Jinggang .

ADVANCES IN MATHEMATICS, 2010, 224 (05) :2052-2093

[8] An extension problem related to the fractional Laplacian [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1245-1260

[9] Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations [J].

Capella, Antonio ;

Davila, Juan ;

Dupaigne, Louis ;

Sire, Yannick .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (08) :1353-1384

[10] Existence of multiple positive weak solutions and estimates for extremal values to a class of elliptic problems with Hardy term and singular nonlinearity [J].

Chen, Yaoping ;

Chen, Jianqing .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 429 (02) :873-900

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