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Model. Anal. Inform. Sist., 2016, Volume 23, Number 1, Pages 41–60 (Mi mais482)  

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

Asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points

S. A. Kashchenkoab

a P.G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
b National Engineering Physics Institute "MEPhI", Moscow

Abstract: For singularly perturbed second order equations the dependence of eigenvalues of the first boundary problem on a small parameter at the highest derivative is studied. The main assumption is that the coefficient at the first derivative in the equation is the sign of the variable. This leads to the emerging of so-called turning points. Asymptotic expansions on the small parameter are obtained for all eigenvalues of the considered boundary problem. It turns out that the expansions are defined by the behavior of coefficients in a neighborhood of turning points only.

Keywords: singularly perturbed equation, turning points, asymptotic, boundary value problem, eigenvalues.

DOI: https://doi.org/10.18255/1818-1015-2016-1-41-60

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Bibliographic databases:

UDC: 517.9
Received: 15.12.2015

Citation: S. A. Kashchenko, “Asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points”, Model. Anal. Inform. Sist., 23:1 (2016), 41–60

Citation in format AMSBIB
\Bibitem{Kas16}
\by S.~A.~Kashchenko
\paper Asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 1
\pages 41--60
\mathnet{http://mi.mathnet.ru/mais482}
\crossref{https://doi.org/10.18255/1818-1015-2016-1-41-60}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3502274}
\elib{http://elibrary.ru/item.asp?id=25475541}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Kaschenko, “Asimptoticheskie razlozheniya sobstvennykh znachenii periodicheskoi i antiperiodicheskoi kraevykh zadach dlya singulyarno vozmuschennykh differentsialnykh uravnenii vtorogo poryadka s tochkami povorota”, Model. i analiz inform. sistem, 23:1 (2016), 61–85  mathnet  crossref  mathscinet  elib
  • Моделирование и анализ информационных систем
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