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Matematicheskie Zametki, 2008, Volume 84, Issue 4, Pages 552–566
DOI: https://doi.org/10.4213/mzm4173
(Mi mzm4173)
 

This article is cited in 10 scientific papers (total in 10 papers)

On the Uniqueness Criterion for Solutions of the Sturm–Liouville Equation

Kh. K. Ishkin

Bashkir State University
References:
Abstract: We consider the Sturm–Liouville equation
$$ -y''+qy=\lambda^2y $$
in an annular domain $K$ from $\mathbb C$ and obtain necessary and sufficient conditions on the potential $q$ under which all solutions of the equation $-y''(z)+q(z)y(z)=\lambda^2y(z)$, $z\in\gamma$, where $\gamma$ is a certain curve, are unique in the domain $K$ for all values of the parameter $\lambda\in\mathbb C$.
Keywords: spectral problem, Sturm–Liouville equation, holomorphic function, uniqueness problem, Bessel function, Rouché theorem, meromorphic function, simple pole.
Received: 14.03.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 4, Pages 515–528
DOI: https://doi.org/10.1134/S000143460809023X
Bibliographic databases:
UDC: 517.927.25
Language: Russian
Citation: Kh. K. Ishkin, “On the Uniqueness Criterion for Solutions of the Sturm–Liouville Equation”, Mat. Zametki, 84:4 (2008), 552–566; Math. Notes, 84:4 (2008), 515–528
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm4173
  • https://www.mathnet.ru/eng/mzm/v84/i4/p552
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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