A critical phenomenon for sublinear elliptic equations in cone–like domains

We study positive supersolutions to an elliptic equation (∗) −∆u = c|x|u, p, s ∈ R, in cone–like domains in R (N ≥ 2). We prove that in the sublinear case p < 1 there exists a critical exponent p∗ < 1 such that equation (∗) has a positive supersolution if and only if −∞ < p < p∗. The value of p∗ is determined explicitly by s and the geometry of the cone.