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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 8, Pages 1350–1355 (Mi zvmmf263)  

This article is cited in 6 scientific papers (total in 6 papers)

Calculating the eigenvalues of the Sturm–Liouville problem with a fractal indefinite weight

A. A. Vladimirov

Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: An efficient method is proposed for calculating the eigenvalues of the boundary value problem $-y"-\lambda\rho y=0,\quad y(0)=y(1)=0$, where $\rho\in\mathring W_2^{-1}[0,1]$ is the generalized derivative of a self-similar function $P\in L_2[0,1]$.

Key words: Sturm–Liouville problem, method for calculating the eigenvalues, fractal indefinite weight function.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:8, 1295–1300

Bibliographic databases:

UDC: 519.624.1
Received: 17.11.2006
Revised: 26.02.2007

Citation: A. A. Vladimirov, “Calculating the eigenvalues of the Sturm–Liouville problem with a fractal indefinite weight”, Zh. Vychisl. Mat. Mat. Fiz., 47:8 (2007), 1350–1355; Comput. Math. Math. Phys., 47:8 (2007), 1295–1300

Citation in format AMSBIB
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\paper Calculating the eigenvalues of the Sturm--Liouville problem with a~fractal indefinite weight
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 8
\pages 1350--1355
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\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 8
\pages 1295--1300
\crossref{https://doi.org/10.1134/S0965542507080076}
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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. A. A. Vladimirov, “On the oscillation theory of the Sturm–Liouville problem with singular coefficients”, Comput. Math. Math. Phys., 49:9 (2009), 1535–1546  mathnet  crossref  zmath  isi  elib  elib
    2. A. A. Vladimirov, I. A. Sheipak, “Asymptotics of the Eigenvalues of the Sturm–Liouville Problem with Discrete Self-Similar Weight”, Math. Notes, 88:5 (2010), 637–646  mathnet  crossref  crossref  mathscinet  isi
    3. A. A. Vladimirov, I. A. Shejpak, “Eigenvalue asymptotics of the problem of high odd order with dicrete self-similar weight”, St. Petersburg Math. J., 24:2 (2013), 263–273  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. 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
    5. Hashimoglu I., “Asymptotics of the Number of Eigenvalues of One-Term Second-Order Operator Equations”, Adv. Differ. Equ., 2015, 335  crossref  mathscinet  isi  elib  scopus
    6. Ben-Reuven M., Zamir I., Gany A., Grinstein D., “Theoretical Modeling of Electrically Operated Ammonium Nitrate Propellant Combustion”, Int. J. Energ. Mater. Chem. Propuls., 18:1 (2019), 67–89  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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