Existence of positive solutions for multi-point boundary value problems on infinite intervals in Banach spaces

In this paper, the cone theory and Mönch fixed point theorem combined with a monotone iterative technique are used to investigate the positive solutions of a class of boundary problems for second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The conditions for the existence of a positive solution are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.