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

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

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
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
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
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
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
5. A. A. Vladimirov, “On the Problem of Oscillation Properties of Positive Differential Operators with Singular Coefficients”, Math. Notes, 100:6 (2016), 790–795
6. A. S. Ivanov, A. M. Savchuk, “Trace of Order $(-1)$ for a String with Singular Weight”, Math. Notes, 102:2 (2017), 164–180
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
8. A. A. Vladimirov, “On a class of singular Sturm–Liouville problems”, Trans. Moscow Math. Soc., 80 (2019), 211–219
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