Multiplicity of Solutions for an Elliptic Problem with Critical Sobolev-Hardy Exponents and Concave-Convex Nonlinearities

被引：0

作者：

Li, Juan ^{[1
]}

Tong, Yuxia ^{[2
]}

机构：

[1] Ningbo Univ, Dept Math, Ningbo 315211, Zhejiang, Peoples R China

[2] Hebei United Univ, Coll Sci, Tangshan 063009, Peoples R China

来源：

JOURNAL OF FUNCTION SPACES | 2014年 / 2014卷

基金：

中国国家自然科学基金;

关键词：

POSITIVE SOLUTIONS;

D O I：

10.1155/2014/180105

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of multiple solutions for the following elliptic problem: -Delta(p)u - mu(vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(p)) = (vertical bar u vertical bar(p)*(t)-2/vertical bar x vertical bar t)u + lambda(vertical bar u vertical bar(q-2)/vertical bar x vertical bar(s))u, u epsilon W-0(1,p)(Omega). We prove that if 1 <= q < p < N, then there is a mu(0), such that for any mu epsilon (0,mu(0)), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result (Azorero and Alonso, 1991).

引用

页数：6

共 11 条

[1]

[Anonymous], J MATH SCI ADV APPL

[2] MULTIPLICITY OF SOLUTIONS FOR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT OR WITH A NONSYMMETRIC TERM [J].

AZORERO, JG ;

ALONSO, IP .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (02) :877-895

[3]

CAFFARELLI L, 1984, COMPOS MATH, V53, P259

[4] Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents [J].

Ghoussoub, N ;

Yuan, C .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (12) :5703-5743

[5]

Hardy G.H, 1988, Inequalities

[6] Multiple positive solutions for a quasilinear elliptic problem involving critical Sobolev-Hardy exponents and concave-convex nonlinearities [J].

Hsu, Tsing-San .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (12) :3934-3944

[7] On the quasilinear elliptic problem with a critical Hardy-Sobolev exponent and a Hardy term [J].

Kang, Dongsheng .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (08) :2432-2444

[8] On the quasilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy terms [J].

Kang, Dongsheng .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (07) :1973-1985

[9]

Lions P-L., 1985, Rev. Mat. Iberoamericana, V1, P145, DOI [DOI 10.4171/RMI/6, 10.4171/rmi/6]

[10]

Rabinowitz P.H., 1986, CBMS Regional Conference Series in Mathematics, V65

← 1 2 →