Existence of positive solutions to fractional elliptic problems with Hardy potential and critical growth

被引：6

作者：

Shang, Xudong ^{[1
]}

Zhang, Jihui ^{[2
]}

Yin, Rong ^{[3
]}

机构：

[1] Nanjing Normal Univ, Taizhou Coll, Sch Math, Taizhou, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China

[3] Nantong Univ, Sch Sci, Nantong, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 01期

基金：

中国国家自然科学基金;

关键词：

concentration compactness principle; critical nonlinearities; fractional Laplacian; Hardy potential; EQUATION; INEQUALITIES; WHOLE;

D O I：

10.1002/mma.5327

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we study the following critical problem involving the fractional Laplacian:(-Delta)su-mu u|x|2s=lambda g(x)up+K(x)u2s*-1,x is an element of RN,where s is an element of (0,1), N > 2s, 0N,s, the sharp constant of the Hardy-Sobolev inequality. For suitable assumptions on g(x) and K(x), we consider the existence and multiplicity of positive solutions depending on the value of p. Moreover, we obtain an existence result for the problem when lambda = 0.

引用

页码：115 / 136

页数：22

共 28 条

[1]

Abdellaoui B, 2004, ADV DIFFERENTIAL EQU, V9, P481

[2]

Abdellaoui B, 2009, CALC VAR PARTIAL DIF, V34, P97, DOI 10.1007/s00526-008-0177-2

[3]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[4]

[Anonymous], 1969, TEOR VEROJATNOST PRI

[5]

[Anonymous], 1996, CAMB TRACTS MATH

[6] Some remarks on the solvability of non-local elliptic problems with the Hardy potential [J].

Barrios, B. ;

Medina, M. ;

Peral, I. .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2014, 16 (04)

[7] On some critical problems for the fractional Laplacian operator [J].

Barrios, B. ;

Colorado, E. ;

de Pablo, A. ;

Sanchez, U. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) :6133-6162

[8] On a semilinear elliptic equation with inverse-square potential [J].

Brezis, Haim ;

Dupaigne, Louis ;

Tesei, Alberto .

SELECTA MATHEMATICA-NEW SERIES, 2005, 11 (01) :1-7

[9]

Bucur C, 2016, LECT NOTES UNIONE MA, V20, P1, DOI 10.1007/978-3-319-28739-3

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

Caffarelli, Luis ;

Silvestre, Luis .

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

← 1 2 3 →