Asymptotic Analysis of the General Solution of a Linear Singularly Perturbed System of Higher-Order Differential Equations with Degenerations
- Authors: Pafyk S.P.1, Yakovets’ V.P.2
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Affiliations:
- Drahomanov National Pedagogic University
- University of Management of Education, Ukrainian National Academy of Pedagogical Sciences
- Issue: Vol 215, No 3 (2016)
- Pages: 350-375
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237598
- DOI: https://doi.org/10.1007/s10958-016-2843-9
- ID: 237598
Cite item
Abstract
We consider a homogeneous system of linear singularly perturbed differential equations of order m with matrix at higher derivatives that becomes singular as the small parameter approaches zero. By using the Newton diagrams, we study the structure of the general solution of the analyzed system and the possibility of construction of its asymptotics in the case where the corresponding characteristic polynomial of the matrix has multiple finite and infinite elementary divisors. The obtained results generalize the results obtained for similar systems of equations of the first and second orders.
About the authors
S. P. Pafyk
Drahomanov National Pedagogic University
Email: Jade.Santos@springer.com
Ukraine, Pyrohov Str., 9, Kyiv, 01030
V. P. Yakovets’
University of Management of Education, Ukrainian National Academy of Pedagogical Sciences
Email: Jade.Santos@springer.com
Ukraine, Artem Str. 52-a, Kyiv, 01601