IJAM, Volume 26, No. 3 (2013)

Abstract. In this paper we investigate the existence and non existence of solutions to the following singular semilinear elliptic system: -\Delta u=\lambda v+\frac{ v^{p}}{\left\vert x\right\vert ^{\alpha}} is a smooth bounded domain in R^N (N \geq 3 ), 0 \in \Omega, \lambda > 0, 0 < \alpha, \beta < N and p,q>1 satisfy the condition \frac{N-\alpha}{p+1}+\frac{N-\beta}{q+1}>N-2. The existence of a nontrivial solution is obtained by variational methods.