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Mat. Zametki, 2008, Volume 84, Issue 4, Pages 552–566 (Mi mz4173)  

This article is cited in 3 scientific papers (total in 3 papers)

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

Kh. K. Ishkin

Bashkir State University

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

DOI: https://doi.org/10.4213/mzm4173

Full text: PDF file (555 kB)
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English version:
Mathematical Notes, 2008, 84:4, 515–528

Bibliographic databases:

UDC: 517.927.25
Received: 14.03.2007

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kh. K. Ishkin, “On a Trivial Monodromy Criterion for the Sturm–Liouville Equation”, Math. Notes, 94:4 (2013), 508–523  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Kh. K. Ishkin, “Localization criterion for the spectrum of the Sturm–Liouville operator on a curve”, St. Petersburg Math. J., 28:1 (2017), 37–63  mathnet  crossref  mathscinet  isi  elib
    3. A. A. Golubkov, “Obratnaya zadacha dlya operatorov Shturma–Liuvillya v kompleksnoi ploskosti”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:2 (2018), 144–156  mathnet  crossref  elib
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