On strictly positive solutions for some semilinear elliptic problems

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.