Asymptotics of eigenvalues of the first boundary-value problem for singularly perturbed second-order differential equation with turning points
- Authors: Kaschenko S.A.1,2
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Affiliations:
- Demidov Yaroslavl State University
- National Research Nuclear University MEPhI
- Issue: Vol 50, No 7 (2016)
- Pages: 636-656
- Section: Article
- URL: https://journals.rcsi.science/0146-4116/article/view/174623
- DOI: https://doi.org/10.3103/S0146411616070105
- ID: 174623
Cite item
Abstract
We consider a second-order linear differential equation of with a small factor at the highest derivative. We study the asymptotic behavior of eigenvalues of the first boundary-value problem (the Dirichlet problem) under the assumption that turning points (points where the coefficient at the first derivative equals to zero) exist. It has been 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.
About the authors
S. A. Kaschenko
Demidov Yaroslavl State University; National Research Nuclear University MEPhI
Author for correspondence.
Email: kasch@uniyar.ac.ru
Russian Federation, ul. Sovetskaya 14, Yaroslavl, 150000; sh. Kashirskoe 31, Moscow, 115409