Solving a singular nonlocal problem with redundant conditions for a system of linear ordinary differential equations

Abstract

A system of linear ordinary differential equations is examined on an infinite or semi-infinite interval. The basic conditions are nonlocal and are specified by a Stieltjes integral; moreover, certain redundant (and also nonlocal) conditions are imposed. At infinity, the solution is required to be bounded. A method for solving such an over-determined problem is proposed and analyzed. The method is numerically stable if an auxiliary problem that replaces the original one is numerically stable.