Existence and uniqueness of positive solution to a boundary value problem for a nonlinear second order functional-differential equation

This work is a continuation of the author’s series of articles devoted to the questions of the existence and uniqueness of positive solutions of boundary value problems for nonlinear functional differential equations of the second order. In this paper, we consider a boundary value problem for one nonlinear functional-differential equation of the second order with homogeneous boundary conditions. Based on the theory of semi-ordered spaces using special topological tools, the existence of a unique positive solution to the problem under study is proved.