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Model. Anal. Inform. Sist., 2015, Volume 22, Number 5, Pages 682–710 (Mi mais467)  

This article is cited in 4 scientific papers (total in 4 papers)

Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points

S. A. Kaschenko

P.G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: We consider a linear differential equation of second order with a small factor at the highest derivative. We study the problem of the asymptotic behavior of the eigenvalues of the first boundary value problem (task Dirichlet) in situation when the turning points (points where the coefficient at the first derivative equals to zero) exist. It is shown that only the behavior of coefficients of the equation in a small neighborhood of the turning points is essential. The main result is a theorem on the limit values of the eigenvalues of the first boundary value problem.

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

DOI: https://doi.org/10.18255/1818-1015-2015-5-682-710

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Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 04.09.2015

Citation: S. A. Kaschenko, “Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points”, Model. Anal. Inform. Sist., 22:5 (2015), 682–710

Citation in format AMSBIB
\Bibitem{Kas15}
\by S.~A.~Kaschenko
\paper Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points
\jour Model. Anal. Inform. Sist.
\yr 2015
\vol 22
\issue 5
\pages 682--710
\mathnet{http://mi.mathnet.ru/mais467}
\crossref{https://doi.org/10.18255/1818-1015-2015-5-682-710}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3499145}
\elib{http://elibrary.ru/item.asp?id=25063578}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Kaschenko, “Asimptoticheskie razlozheniya sobstvennykh chisel pervoi kraevoi zadachi dlya singulyarno vozmuschennogo differentsialnogo uravneniya vtorogo poryadka s tochkami povorota”, Model. i analiz inform. sistem, 23:1 (2016), 41–60  mathnet  crossref  mathscinet  elib
    2. 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
    3. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Many-circuit canard trajectories and their applications”, Izv. Math., 81:4 (2017), 771–817  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. S. A. Kashchenko, “Asymptotic Expansions of Eigenvalues of the First Boundary-Value Problem For Singularly Perturbed Second-Order Differential Equation With Turning Points”, Autom. Control Comp. Sci., 51:7 (2017), 592–605  crossref  isi  scopus
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