Geodesic
Bounded solutions of families of systems of differential equations and their approximation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 29-47 
D. S. Dzhumabaev. Bounded solutions of families of systems of differential equations and their approximation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 29-47. http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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