The boundary-value problem for the linear degenerated singularly perturbed system of differential equations of the second order (in Ukrainian)

Author
. B. Vira
Nizhyn Gogol State University, Nizhyn, Ukraine
Abstract
It is investigated the possibility of construction of the asymptotic solution of the boundary-value problem for the linear singularly perturbed system of differential equations of the second order with identically degenerated matrix at the derivatives of higher order in case than boundary bundle of matrixes has simple spectrum. It was obtained the conditions of the existence and uniqueness of the solution of this boundary-value problem and its asymptotic is constructed in form of power series with degrees of small parameter.
Keywords
boundary-value problem; system of differential equations of the second order; the conditions of the existence and uniqueness
DOI
doi:10.15330/ms.47.2.185-195
Reference
1. Yakovets V.P., Vira M.B. On the construction of asymptotic solutions two-point boundary problems for degenerate singularly perturbed systems of differential equations// Nonlinear Oscillations. 2010. V.13, 2. P. 272286. (in Ukarainian)

2. Vira M.B. Two-point boundary value problem for degenerate singularly perturbed system of differential equations in case multiple spectrum of the main operator// Proceedings of IAPM NAS of Ukraine. 2009. V.18. P. 1928. (in Ukarainian)

3. Vira M.B. On the construction of an asymptotic solution two-point boundary value problem for linear singularly perturbed differential algebraic system// Dynamic systems: interdepartmental scientific compilation. 2011. V.1(29), 1. P. 1530. (in Ukarainian)

4. Vira M.B. On constructing of asymptotic solution of the boundary-value problem for the linear degenerated singularly perturbed system of differential equations in critical case// Proceedings of IAPM NAS of Ukraine. 2013. V.26. P. 3139. (in Russian)

5. Samoilenko A.M., Shkil M.I., Yakovets V.P. Linear differential systems degenerate equations Kuiv: Vyshcha Schkola, 2000. 294 p. (in Ukarainian)

Pages
185-195
Volume
47
Issue
2
Year
2017
Journal
Matematychni Studii
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