This article is cited in 13 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.

UDC: 517.942

MSC: Primary 34B25, 47E05; Secondary 47A10

Received: 23.10.1978

 English version: Mathematics of the USSR-Sbornik, 1981, 38:1, 127–141

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