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

Author 
VyraMaryna@mail.ru
Nizhyn Gogol State University, Nizhyn, Ukraine

Abstract 
It is investigated the possibility of construction of the asymptotic solution of the boundaryvalue
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 boundaryvalue problem and its asymptotic is constructed in
form of power series with degrees of small parameter.

Keywords 
boundaryvalue problem; system of differential equations of the second order; the conditions of
the existence and uniqueness

DOI 
doi:10.15330/ms.47.2.185195

Reference 
1. Yakovets V.P., Vira M.B. On the construction of asymptotic solutions twopoint boundary problems for
degenerate singularly perturbed systems of differential equations// Nonlinear Oscillations. – 2010. – V.13,
¹2. – P. 272–286. (in Ukarainian)
2. Vira M.B. Twopoint 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. 19–28. (in Ukarainian) 3. Vira M.B. On the construction of an asymptotic solution twopoint boundary value problem for linear singularly perturbed differential algebraic system// Dynamic systems: interdepartmental scientific compilation. — 2011. — V.1(29), ¹1. – P. 15–30. (in Ukarainian) 4. Vira M.B. On constructing of asymptotic solution of the boundaryvalue problem for the linear degenerated singularly perturbed system of differential equations in critical case// Proceedings of IAPM NAS of Ukraine. – 2013. – V.26. – P. 31–39. (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 
185195

Volume 
47

Issue 
2

Year 
2017

Journal 
Matematychni Studii

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