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 ori...

Full description

Saved in:
Bibliographic Details
Published inҚарағанды университетінің хабаршысы. Математика сериясы Vol. 117; no. 1; pp. 187 - 198
Main Authors Uteshova, R., Kokotova, Y.
Format Journal Article
LanguageEnglish
Published Academician Ye.A. Buketov Karaganda University 01.01.2025
Subjects
approximation
bounded solution
linear differential equation
parameterization method
singular boundary value problem
well-posedness
Online AccessGet full text
ISSN2518-7929
2663-5011
DOI10.31489/2025m1/187-198

Cover

More Information
Summary: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.
ISSN:2518-7929
2663-5011
DOI:10.31489/2025m1/187-198