On a singular elliptic equation

In this paper, we study the singular elliptic equation Lu + K(x)u^p = 0. where L is a uniformly elliptic operator of divergence form, p > 1 and 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 C₁, C₂ such that C₁ |x|^σ ≥ K(x) ≥ C₂ | x |^σ near the origin for some σ ≥ -2 (with no other condition on the gradient of K). In fact, an integral condition is derived.