Positive solutions for a class of singular elliptic system

• Main Author: Ling Mi
• Format: Article
• Language: English
• Published: University of Szeged 2017-04-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: singular elliptic systems; dirichlet problems; existence; boundary behavior; uniqueness
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5570

In this paper, we mainly study the existence, boundary behavior and uniqueness of solutions for the following singular elliptic systems involving weights $-\triangle u =w(x)u^{-p}v^{-q}, -\triangle v =\lambda(x)u^{-r}v^{-s}, u>0, v>0, \ x\in \Omega, \ u|_{\partial \Omega}=v|_{\partial \Omega}=0$, where $\Omega$ is a bounded domain with a smooth boundary in $\mathbb R^N\ (N\geq 2)$, $p, s \geq 0,$ $q, r > 0$ and the weight functions $w(x), \lambda(x) \in C^{\alpha}(\bar{\Omega})$ which are positive in $\Omega$ and may be blow-up on the boundary.