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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 3, Pages 9–15 (Mi ufa295)  

This article is cited in 2 scientific papers (total in 2 papers)

On a new approach for studying asymptotic behavior of solutions to singular differential equations

N. F. Valeeva, E. A. Nazirovab, Ya. T. Sultanaevc

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa, Russia
b Bashkir State University, Ufa, Russia
c Bashkir State Pedagogical University, Ufa, Russia

Abstract: In the work we propose a new approach for studying the asymptotic behavior for large $x$ of the solutions to singular linear two-terms differential equations
$$ -\frac{d^n}{dx^n}y(x,\lambda)+\lambda q(x)y(x,\lambda)=0 $$
with a potential $q(x)$ non-regular growing as $x\to\infty$. The idea of constructing the asymptotics for the solutions of singular linear differential equations and its effectiveness is demonstrated for 4th order equations with an oscillating potential.

Keywords: spectral theory of differential operators, asymptotic formulae for solutions to differential equations.

Full text: PDF file (173 kB)
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English version:
Ufa Mathematical Journal, 2015, 7:3, 9–14 (PDF, 303 kB); https://doi.org/10.13108/2015-7-3-9

Bibliographic databases:

UDC: 517.928
MSC: 34K08
Received: 24.07.2015

Citation: N. F. Valeev, E. A. Nazirova, Ya. T. Sultanaev, “On a new approach for studying asymptotic behavior of solutions to singular differential equations”, Ufimsk. Mat. Zh., 7:3 (2015), 9–15; Ufa Math. J., 7:3 (2015), 9–14

Citation in format AMSBIB
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\by N.~F.~Valeev, E.~A.~Nazirova, Ya.~T.~Sultanaev
\paper On a~new approach for studying asymptotic behavior of solutions to singular differential equations
\jour Ufimsk. Mat. Zh.
\yr 2015
\vol 7
\issue 3
\pages 9--15
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\elib{http://elibrary.ru/item.asp?id=24716947}
\transl
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 3
\pages 9--14
\crossref{https://doi.org/10.13108/2015-7-3-9}
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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. N. F. Valeev, A. Eskermesuly, Ya. T. Sultanaev, “On the Deficiency Index of a Differential Operator with Fast Oscillating Coefficients”, Math. Notes, 100:3 (2016), 486–490  mathnet  crossref  crossref  mathscinet  isi  elib
    2. N. F. Valeev, O. V. Myakinova, Ya. T. Sultanaev, “On the Asymptotics of Solutions of a Singular $n$th-Order Differential Equation with Nonregular Coefficients”, Math. Notes, 104:4 (2018), 606–611  mathnet  crossref  crossref  isi  elib
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