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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1609–1621 (Mi zvmmf4753)  

This article is cited in 8 scientific papers (total in 8 papers)

On the oscillation theory of the Sturm–Liouville problem with singular coefficients

A. A. Vladimirovab

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia (MFTI)
b Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: The spectral Sturm–Liouville problem with distribution coefficients is examined. It is shown that the basic results concerning the number and the location of the zeros of eigenfunctions that are known in the smooth case remain valid in the general situation. The Chebyshev properties of systems of eigenfunctions are also investigated in the case where the weight function is positive.

Key words: singular Sturm–Liouville problem, oscillation of eigenfunctions, Chebyshev system of functions.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1535–1546

Bibliographic databases:

UDC: 519.624.2
Received: 25.11.2008
Revised: 20.02.2009

Citation: A. A. Vladimirov, “On the oscillation theory of the Sturm–Liouville problem with singular coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1609–1621; Comput. Math. Math. Phys., 49:9 (2009), 1535–1546

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. Ben Amara, A. A. Vladimirov, A. A. Shkalikov, “Spectral and Oscillatory Properties of a Linear Pencil of Fourth-Order Differential Operators”, Math. Notes, 94:1 (2013), 49–59  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Karulina E.S., Vladimirov A.A., “The Sturm-Liouville Problem with Singular Potential and the Extrema of the First Eigenvalue”, Differential and Difference Equations and Applications 2012, Tatra Mountains Mathematical Publications, 54, eds. Diblik J., Ruzickova M., Slovak Academy Sciences Mathematical Institute, 2013, 101–118  crossref  mathscinet  isi  elib
    3. A. A. Vladimirov, I. A. Sheipak, “On the Neumann Problem for the Sturm–Liouville Equation with Cantor-Type Self-Similar Weight”, Funct. Anal. Appl., 47:4 (2013), 261–270  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. N. V. Rastegaev, “On spectral asymptotics of the Neumann problem for the Sturm–Liouville equation with self-similar generalized Cantor type weight”, J. Math. Sci. (N. Y.), 210:6 (2015), 814–821  mathnet  crossref
    5. A. A. Vladimirov, “On the Problem of Oscillation Properties of Positive Differential Operators with Singular Coefficients”, Math. Notes, 100:6 (2016), 790–795  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. S. Ivanov, A. M. Savchuk, “Trace of Order $(-1)$ for a String with Singular Weight”, Math. Notes, 102:2 (2017), 164–180  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. N. V. Rastegaev, “On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type”, Funct. Anal. Appl., 52:1 (2018), 70–73  mathnet  crossref  crossref  isi  elib
    8. A. A. Vladimirov, “On a class of singular Sturm–Liouville problems”, Trans. Moscow Math. Soc., 80 (2019), 211–219  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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