Positive solutions of boundary value problems for second-order singular nonlinear differential equations

New existence results are presented for the singular second-order nonlinear boundary value problems u″+g(t)f(u)=0, 0<t<1, αu(0)−βu′(0)=0, γu(1)+δu′(1)=0 under the conditions 0≤f0+<M1, m1<f∞−≤∞ or 0≤f∞+<M1, m1<f0−≤∞, where\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{gathered} f_0^ + = \overline {\lim } _{u \to 0} f(u)/u, f_\infty ^ - = \underline {\lim } _{u \to \infty } f(u)/u, f_0^ - = \hfill \\ \underline {\lim } _{u \to 0} f(u)/u, f_\infty ^ + = \overline {\lim } _{u \to \infty } f(u)/u \hfill \\ \end{gathered} $$ \end{document}, g may be singular at t=0 and/or t=1. The proof uses a fixed point theorem in cone theory.