In this paper, we study the singular elliptic equation L u + K ( x ) u p = 0 Lu + K(x){u^p} = 0 , where L L is a uniformly elliptic operator of divergence form, p > 1 p > 1 and K ( x ) K(x) has a singularity at the origin. We prove that this equation does not possess any positive (local) solution in any punctured neighborhood of the origin if there exist two constants C 1 {C_1} , C 2 {C_2} such that C 1 | x | σ ⩾ K ( x ) ⩾ C 2 | x | σ {C_1}|x{|^\sigma } \geqslant K(x) \geqslant {C_2}|x{|^\sigma } near the origin for some σ ⩽ − 2 \sigma \leqslant - 2 (with no other condition on the gradient of K K ). In fact, an integral condition is derived.