Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775276 | Journal of Mathematical Analysis and Applications | 2017 | 27 Pages |
Abstract
In this paper, we deal with the following singular elliptic system:{âÎu+α|âu|2u=pp+qa(x)|v|q|u|pâ2u+f,xâRN,âÎv+β|âv|2v=qp+qa(x)|u|p|v|qâ2v+g,xâRN, where Nâ¥3, α,β>N+24, p,q>1 and p+qâ¤N+2Nâ2. We show through the sub- and supersolutions method, the existence of a nonnegative solution for an approximated system. The limit of the approximated solution is a positive solution. In the case, α=β=0, p=q and f=g, we prove the uniqueness of a solution. Among others, we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle, a minimization method and with the help of Nehari manifold. The proofs rely on the concentration-compactness principle.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mohamed Benrhouma,