Acta mathematica scientia, Series B >
EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS
Received date: 2011-10-10
Revised date: 2012-02-24
Online published: 2013-01-20
Supported by
This project is supported by NSFC (10771085), Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education, and the 985 Program of Jilin University.
The main purpose of this paper is to establish the existence of multiple so-lutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions.
LI Yuan-Xiao , GAO Wen-Jie . EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS[J]. Acta mathematica scientia, Series B, 2013 , 33(1) : 107 -121 . DOI: 10.1016/S0252-9602(12)60197-0
[1] Ambrosetti A, Brezis H, Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J Funct Anal, 1994, 122: 519–543
[2] Cao D, Han P. Solutions for semilinear elliptic equations with critical exponents and Hardy potential. J Differ Equ, 2004, 205: 521–537
[3] Chen J. Multiple positive solutions for a class of nonlinear elliptic equations. J Math Anal Appl, 2004, 295: 341–354
[4] Ferrero A, Gazzola F. Existence of solutions for singular critical growth semilinear elliptic equations. J Differ Equ, 2001, 177: 494–522
[5] Han P, Liu Z. Solutions for a singular critical growth problem with a weight. J Math Anal Appl, 2007, 327: 1075–1085
[6] Bouchekif M, Matallah A. Multiple positive solutions for elliptic equations involving a concave term and critical Sobolev-Hardy exponent. Appl Math Lett, 2009, 22: 268–275
[7] Ghoussoub N, Kang X S. Hardy-Sobolev critical elliptic equations with boundary singularities. Ann Inst H Poincar´e Anal Non Linéaire, 2004, 21: 769–793
/
| 〈 |
|
〉 |