Abstract: This paper concerns a class of semilinear elliptic equations with a twofold singularity:$-\operatorname{div}[M(x) \nabla u(x)]=|x|^{-\gamma} / u(x)$, Where $\Omega \subset \mathbb{R}^{n}$ a bounded domain containing the origin. Under the assumptions that the exponent satisfies $-n<-\gamma<0$ and that the coefficient matrix $M(x)$ is uniformly elliptic with uniformly bounded determinant, we prove the existence of a positive solution to this problem in the Sobolev space $H_{0}^{1}(\Omega)$.

Key words: Hardy potential, negative exponent, singular equation