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Matematicheskie Zametki, 2024, Volume 116, Issue 2, Pages 266–289
DOI: https://doi.org/10.4213/mzm14398
(Mi mzm14398)
 

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic representations of solutions of $n\times n$ systems of ordinary differential equations with a large parameter

A. P. Kosarevab, A. A. Shkalikovab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
References:
Abstract: The paper considers $n \times n$ systems of ordinary differential equations of the form
$$ y'-By-C(\cdot, \lambda)y=\lambda Ay, \qquad y=y(x), \quad x \in [0, 1], $$
where $A=\operatorname{diag}\{a_1(x), \dots, a_n(x)\}$, $B=\{b_{jk}(x)\}_{j, k=1}^n$, and $C= \{c_{jk}(x, \lambda)\}_{j, k=1}^n$. All functions in these matrices are complex-valued and integrable over $x \in [0, 1]$, and $\|c_{jk}(\cdot, \lambda)\|_{L_1} \to 0$ as $\lambda \to \infty$. The theorems proved in the paper generalize the results of the classical Birkhoff–Tamarkin–Langer theory concerning asymptotic representations of fundamental solutions in sectors and half-strips of the complex plane as $\lambda \to \infty$. The focus is on the minimality of the smoothness requirements on the coefficients.
Keywords: asymptotics of solutions of ordinary differential equations and systems, spectral asymptotics, Birkhoff asymptotics.
Funding agency Grant number
Russian Foundation for Basic Research 20-11-20261
This work was supported by the Russian Foundation for Basic Research under grant 20-11-20261.
Received: 16.05.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 2, Pages 283–302
DOI: https://doi.org/10.1134/S000143462407023X
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. P. Kosarev, A. A. Shkalikov, “Asymptotic representations of solutions of $n\times n$ systems of ordinary differential equations with a large parameter”, Mat. Zametki, 116:2 (2024), 266–289; Math. Notes, 116:2 (2024), 283–302
Citation in format AMSBIB
\Bibitem{KosShk24}
\by A.~P.~Kosarev, A.~A.~Shkalikov
\paper Asymptotic representations of solutions of $n\times n$ systems of ordinary differential equations with a large parameter
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 2
\pages 266--289
\mathnet{http://mi.mathnet.ru/mzm14398}
\crossref{https://doi.org/10.4213/mzm14398}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 2
\pages 283--302
\crossref{https://doi.org/10.1134/S000143462407023X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85207215746}
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  • https://doi.org/10.4213/mzm14398
  • https://www.mathnet.ru/eng/mzm/v116/i2/p266
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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