Positive solutions to boundary value problems for second-order ordinary differential equations with singular nonlinearities (Q1266939)

The existence of positive solutions to periodic boundary value problems and of infinitely many positive solutions to Sturm-Liouville problems is proved for the equation \(x''+g(x) =p(t,x,x')\) under a superlinear condition imposed on \(g\) when \(x\to \infty\). The proof is based on the continuation theorem in the absence of a priori bounds given by \textit{A. Capietto}, \textit{J. Mawhin} and \textit{F. Zanolin} [J. Differ. Equations 88, No. 2, 347-395 (1990; Zbl 0718.34053)].