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This article is cited in 11 scientific papers (total in 11 papers)
The asymptotic expansion of the spectrum of a Sturm–Liouville operator
Kh. Kh. Murtazin, T. G. Amangil'din
Abstract:
This paper studies the properties of the spectrum of the problem
\begin{gather*}
-y''(x)+q(x)y(x)=\lambda y(x),\qquad x > 0,\\
y(0)=0,\quad y(x)\in L_2[0,\infty),
\end{gather*}
under the assumption that $q(x)$ grows like a power of $x$ at $\infty$, while allowing that $q(x)$ may have a nonintegrable singularity at $0$. A result which lets one write down the first few terms of an asymptotic series for the eigenvalues is obtained.
Bibliography: 8 titles.
Received: 23.10.1978
Citation:
Kh. Kh. Murtazin, T. G. Amangil'din, “The asymptotic expansion of the spectrum of a Sturm–Liouville operator”, Mat. Sb. (N.S.), 110(152):1(9) (1979), 135–149; Math. USSR-Sb., 38:1 (1981), 127–141
Linking options:
https://www.mathnet.ru/eng/sm2436https://doi.org/10.1070/SM1981v038n01ABEH001221 https://www.mathnet.ru/eng/sm/v152/i1/p135
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Abstract page: | 504 | Russian version PDF: | 231 | English version PDF: | 14 | References: | 30 | First page: | 1 |
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