Existence of solutions for critical elliptic systems with boundary singularities
This article concerns the existence of positive solutions to the nonlinear elliptic system involving critical Hardy-Sobolev exponent $$displaylines{ -Delta u= frac{2lambdaalpha}{alpha+eta} frac{u^{alpha-1} v^eta}{|pi(x)|^s}- u^p, quad hbox{in } Omega,cr -Delta v= frac{2lambdaeta}{alpha+eta} fr...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-04-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/109/abstr.html |
| Summary: | This article concerns the existence of positive solutions to the nonlinear elliptic system involving critical Hardy-Sobolev exponent $$displaylines{ -Delta u= frac{2lambdaalpha}{alpha+eta} frac{u^{alpha-1} v^eta}{|pi(x)|^s}- u^p, quad hbox{in } Omega,cr -Delta v= frac{2lambdaeta}{alpha+eta} frac{u^alpha v^{eta-1}}{|pi(x)|^s}- v^p, quad hbox{in } Omega,cr u>0,quad v>0, quad hbox{in } Omega,cr u=v=0, quad hbox{on } partialOmega, }$$ where $Ngeq 4$ and $Omega$ is a $C^1$ bounded domain in $mathbb{R}^N$, $0<s<2$, $alpha+eta=2^*(s)=frac{2(N-s)}{N-2}$, $alpha,eta>1$, $lambda>0$ and $1leq p<frac{N}{N-2}$. |
|---|---|
| ISSN: | 1072-6691 |