FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 5, PAGES 29-47

**Bounded solutions of families of systems of differential equations and
their approximation**

D. S. Dzhumabaev

Abstract

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In the paper, we consider the problem of finding a bounded
solution of a one-parametric family of systems of ordinary
differential equations.
Using the parametrization method, we prove necessary and sufficient
conditions for the existence of a unique solution of the problem
considered that is bounded on the whole axis in terms of
a two-sided infinite block-band matrix composed with respect to
integrals over intervals of length $h\; >\; 0$ the matrix of the system of differential
equations.
Also, we construct a family of two-point boundary-value problems
on a finite interval that approximate the problem of finding the
bounded solution and finds an interconnection between the correct
solvability of the initial and approximating problems.

Location: http://mech.math.msu.su/~fpm/eng/k06/k065/k06504h.htm

Last modified: February 21, 2007