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Matematicheskie Zametki, 2010, Volume 87, Issue 2, Pages 311–315
DOI: https://doi.org/10.4213/mzm8594
(Mi mzm8594)
 

This article is cited in 20 scientific papers (total in 20 papers)

Brief Communications

Resolvent Convergence of Sturm–Liouville Operators with Singular Potentials

A. S. Goryunov, V. A. Mikhailets

Institute of Mathematics, Ukrainian National Academy of Sciences
References:
Keywords: Sturm–Liouville operator, resolvent convergence of operators, singular potential, quasidifferential expression, quasiderivative, Green function, Green matrix.
Received: 27.01.2010
English version:
Mathematical Notes, 2010, Volume 87, Issue 2, Pages 287–292
DOI: https://doi.org/10.1134/S0001434610010372
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. S. Goryunov, V. A. Mikhailets, “Resolvent Convergence of Sturm–Liouville Operators with Singular Potentials”, Mat. Zametki, 87:2 (2010), 311–315; Math. Notes, 87:2 (2010), 287–292
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm8594
  • https://doi.org/10.4213/mzm8594
  • https://www.mathnet.ru/eng/mzm/v87/i2/p311
  • This publication is cited in the following 20 articles:
    1. Vladimir Mikhailets, Olena Atlasiuk, “The solvability of inhomogeneous boundary-value problems in Sobolev spaces”, Banach J. Math. Anal., 18:2 (2024)  crossref
    2. Fritz Gesztesy, Roger Nichols, “Strict domain monotonicity of the principal eigenvalue and a characterization of lower boundedness for the Friedrichs extension of four-coefficient Sturm–Liouville operators”, Acta Sci. Math. (Szeged), 88:1-2 (2022), 189  crossref
    3. Masliuk H., Soldatov V., “One-Dimensional Parameter-Dependent Boundary-Value Problems in Holder Spaces”, Methods Funct. Anal. Topol., 24:2 (2018), 143–151  mathscinet  isi
    4. Mikhailets V.A., Pelekhata O.B., Reva N.V., “Limit Theorems For the Solutions of Boundary-Value Problems”, Ukr. Math. J., 70:2 (2018), 243–251  crossref  mathscinet  isi  scopus
    5. Hnyp Y., Mikhailets V., Murach A., “Parameter-Dependent One-Dimensional Boundary-Value Problems in Sobolev Spaces”, Electron. J. Differ. Equ., 2017, 81  mathscinet  zmath  isi
    6. Mikhailets V., Murach A., Novikov V., “Localization Principles For Schrodinger Operator With a Singular Matrix Potential”, Methods Funct. Anal. Topol., 23:4 (2017), 367–377  mathscinet  zmath  isi
    7. Maslyuk H.O., “Continuity of the Solutions of One-Dimensional Boundary-Value Problems in Holder Spaces With Respect to the Parameter”, Ukr. Math. J., 69:1 (2017), 101–110  crossref  mathscinet  isi  scopus
    8. Hnyp E.V., “Continuity of the Solutions of One-Dimensional Boundary-Value Problems with Respect to the Parameter in the Slobodetskii Spaces”, Ukr. Math. J., 68:6 (2016), 849–861  crossref  mathscinet  isi  scopus
    9. Mikhailets V., Murach A., Soldatov V., “a Criterion For Continuity in a Parameter of Solutions To Generic Boundary-Value Problems For Higher-Order Differential Systems”, Methods Funct. Anal. Topol., 22:4 (2016), 375–386  mathscinet  zmath  isi
    10. Mikhailets V.A., Murach A.A., Soldatov V., “Continuity in a parameter of solutions to generic boundary-value problems”, Electron. J. Qual. Theory Differ., 2016, no. 87  crossref  mathscinet  isi  elib  scopus
    11. Gnyp E.V., Kodlyuk T.I., Mikhailets V.A., “Fredholm Boundary-Value Problems With Parameter in Sobolev Spaces”, Ukr. Math. J., 67:5 (2015), 658–667  crossref  mathscinet  zmath  isi  scopus
    12. Horyunov A.S., “Convergence and Approximation of the Sturm-Liouville Operators With Potentials-Distributions”, Ukr. Math. J., 67:5 (2015), 680–689  crossref  mathscinet  zmath  isi  scopus
    13. Soldatov V.O., “on the Continuity in a Parameter For the Solutions of Boundary-Value Problems Total With Respect To the Spaces C ((N Plus R))[a, B]”, Ukr. Math. J., 67:5 (2015), 785–794  crossref  mathscinet  zmath  isi  scopus
    14. Vladimir A. Mikhailets, Ganna A. Chekhanova, “Limit theorems for general one-dimensional boundary-value problems”, J Math Sci, 204:3 (2015), 333  crossref
    15. Eckhardt J. Gesztesy F. Nichols R. Teschl G., “Supersymmetry and Schrodinger-Type Operators With Distributional Matrix-Valued Potentials”, J. Spectr. Theory, 4:4 (2014), 715–768  crossref  mathscinet  zmath  isi  scopus
    16. Golovaty Yu., “1D Schrödinger operators with short range interactions: two-scale regularization of distributional potentials”, Integral Equations Operator Theory, 75:3 (2013), 341–362  crossref  mathscinet  zmath  isi  elib  scopus
    17. Eckhardt J., Teschl G., “Sturm-Liouville Operators with Measure-Valued Coefficients”, J. Anal. Math., 120 (2013), 151–224  crossref  mathscinet  zmath  isi  elib  scopus
    18. Kodlyuk T.I., Mikhailets V.A., Reva N.V., “Limit Theorems for One-Dimensional Boundary-Value Problems”, Ukr. Math. J., 65:1 (2013), 77–90  crossref  mathscinet  zmath  isi  scopus
    19. Goriunov A., Mikhailets V., Pankrashkin K., “Formally Self-Adjoint Quasi-Differential Operators and Boundary-Value Problems”, Electron. J. Differ. Equ., 2013, 101  mathscinet  zmath  isi  elib
    20. Goryunov A.S., Mikhailets V.A., “Regularization of two-term differential equations with singular coefficients by quasiderivatives”, Ukr. Math. J., 63:9 (2012), 1361–1378  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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