On strictly positive solutions for some semilinear elliptic problems

Let B be a ball in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{N}}$$\end{document}, 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${-\Delta u=m(x) u^{p}}$$\end{document} in B, u = 0 on ∂B.