Approximation of a singular boundary value problem for a linear differential equation

This paper addresses the approximation of a bounded (on the entire real axis) solution of a linear ordinary differential equation, where the matrix approaches zero as t →∓∞ and the right-hand side is bounded with a weight. We construct regular two-point boundary value problems to approximate the original problem, assuming the matrix and the right-hand side, both weighted, are constant in the limit. An approximation estimate is provided. The relationship between the well-posedness of the singular boundary value problem and the well-posedness of an approximating regular problem is established.