FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 21-39

**On the unique solvability of a family of two-point boundary-value
problems for systems of ordinary differential equations**

A. T. Asanova

Abstract

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We consider a family of two-point boundary-value problems for
systems of ordinary differential equations with functional parameters.
This family is the result of the reduction of a boundary-value problem
with nonlocal condition for a system of second-order quasilinear
hyperbolic equations by introduction of additional functions.
Using the parametrization method, we establish necessary and
sufficient conditions of the unique solvability of the family of
two-point boundary-value problems for a linear system in terms of
initial data.
We also prove sufficient conditions of the unique solvability of the
problem considered and propose an algorithm for its solution.

Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06402h.htm

Last modified: February 17, 2007