Existence of Solutions for Semilinear Nonlocal Elliptic Problems via a Bolzano Theorem

In this paper we deal with the existence of positive solutions for the following nonlocal type of problems \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\everymath{\displaystyle} \left\{ \begin{array}{l@{\quad}l} -\Delta u = \frac{\sigma}{( \int_{\varOmega} g(u)\, dx )^p} f(u) & \mbox{in}\ \varOmega, \\[3mm] u>0 & \mbox{in}\ \varOmega, \\[1mm] u=0 & \mbox{on}\ \partial\varOmega, \end{array} \right. $$\end{document} where Ω is a bounded smooth domain in ℝN (N≥1), f,g are continuous positive functions, σ>0 and p∈ℝ.