Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (1): 107-121.doi: 10.1016/S0252-9602(12)60197-0

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EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS

 LI Yuan-Xiao, GAO Wen-Jie   

  1. College of Science, Henan University of Technology, Zhengzhou 450001, China; Institute of Mathematics, Jilin University, Changchun 130012, China
  • Received:2011-10-10 Revised:2012-02-24 Online:2013-01-20 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.

Abstract:

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.

Key words: singular elliptic system, concave-convex nonlinearities, positive solution, Ne-hari manifold, critical Sobolev-Hardy exponent

CLC Number: 

  • 35J61
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