On strictly positive solutions for some semilinear elliptic problems

Abstract

Let B be a ball in \({\mathbb{R}^{N}}\), N ≥ 1, let m be a possibly discontinuous and unbounded function that changes sign in B and let 0 < p < 1. We study existence and nonexistence of strictly positive solutions for semilinear elliptic problems of the form \({-\Delta u=m(x) u^{p}}\) in B, u = 0 on ∂B.