Some existence principles and some general results for singular nonlinear two point boundary value problems (Q1191769)

The paper is devoted to the study of existence of solutions for singular second order nonlinear two-point boundary value problems of the form \((1/p(t))(p(t)y'(t))'+q(t)f(t,y)=0\), \(0<t<1\), where \(\lim_{y\to 0+}f(t,y)=+\infty\), uniformly on compact subsets of (0,1), and with either (i) \(y(1)=0\), \(\lim_{t\to 0+}p(t)y'(t)=0\); or (ii) \(y(0)=0\), \(y(1)=0\). Also, existence principles are presented for the general two- point boundary value problem for \((1/p(t))(p(t)y'))'+q(t)f(t,y(t)\), \(p(t)y'(t))=0\), \(0<t<1\), where \(f\) is assumed continuous. The proof uses the nonlinear alternative of Leray-Schauder. For a related work see \textit{H. Wang} [Nonlinear Anal., Theory Methods Appl. 18, No. 7, 649-655 (1992)].