Boundary value problems for singular second-order functional differential equations
A fixed-point theorem on cones is used to obtain existence of positive solutions to the boundary value problem \(y''(x) + f(x,y(r(x))) = 0\), \(0 < x < 1\), \(\alpha y'(x) - \beta y(x) = \mu(x)\), \(x \in [a,0]\), \(\gamma y'(x) + \delta y(x) = \nu (x)\), \(x \in [1,b]\), in the case \(f(x,y) \to \infty\) for \(y \to 0\). A uniqueness result is also given. The results extend those of \textit{J. A. Gatica}, \textit{V. Oliker} and \textit{P. Waltman} [J. Differ. Equations 79, 62-78 (1989; Zbl 0685.34017)].
second order equations with deviating argument
scientific article; zbMATH DE number 721017
scientific article