A. M. Savchuk, “On the Eigenvalues and Eigenfunctions of the Sturm–Liouville Operator with a Singular Potential”, Mat. Zametki, 69:2 (2001), 277–285; Math. Notes, 69:2 (2001), 245

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Matematicheskie Zametki, 2001, Volume 69, Issue 2, Pages 277–285
DOI: https://doi.org/10.4213/mzm502 (Mi mzm502)

This article is cited in 34 scientific papers (total in 34 papers)

On the Eigenvalues and Eigenfunctions of the Sturm–Liouville Operator with a Singular Potential

A. M. Savchuk

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (177 kB) Citations (34)

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DOI: https://doi.org/10.4213/mzm502

Abstract: In this paper we consider the Sturm–Liouville operators generated by the differential expression

- y + q (x) y

$-y+q(x)y$ and by Dirichlet boundary conditions on the closed interval

[0, π]

$[0,\pi]$ . Here

q (x)

$q(x)$ is a distribution of first order, i.e.,

\int q (x) d x \in L_{2} [0, π]

$\int q(x)dx\in L_2[0,\pi]$ . Asymptotic formulas for the eigenvalues and eigenfunctions of such operators which depend on the smoothness degree of

q (x)

$q(x)$ are obtained.

Received: 29.05.2000
Revised: 05.07.2000

English version:
Mathematical Notes, 2001, Volume 69, Issue 2, Pages 245–252
DOI: https://doi.org/10.1023/A:1002880520696

Bibliographic databases:

UDC: 517.9+517.43

Language: Russian

Citation: A. M. Savchuk, “On the Eigenvalues and Eigenfunctions of the Sturm–Liouville Operator with a Singular Potential”, Mat. Zametki, 69:2 (2001), 277–285; Math. Notes, 69:2 (2001), 245–252

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm502

https://doi.org/10.4213/mzm502

https://www.mathnet.ru/eng/mzm/v69/i2/p277

This publication is cited in the following 34 articles:

M. Yu. Vatolkin, “Issledovanie asimptotiki sobstvennykh znachenii odnoi kvazidifferentsialnoi kraevoi zadachi vtorogo poryadka”, Izv. vuzov. Matem., 2024, no. 3, 15–37
Michael Ruzhansky, Serikbol Shaimardan, Alibek Yeskermessuly, “Wave equation for Sturm-Liouville operator with singular potentials”, Journal of Mathematical Analysis and Applications, 531:1 (2024), 127783
Alibek Yeskermessuly, Trends in Mathematics, 4, Modern Problems in PDEs and Applications, 2024, 175
M. Yu. Vatolkin, “Investigation of the Asymptotics of the Eigenvalues of a Second-Order Quasidifferential Boundary Value Problem”, Russ Math., 68:3 (2024), 11
M. Yu. Vatolkin, “On the Approximation of the First Eigenvalue of Some Boundary Value Problems”, Comput. Math. and Math. Phys., 64:6 (2024), 1224
M. Yu. Vatolkin, “Issledovanie razmernosti spektralnoi proektsii samosopryazhennogo kvazidifferentsialnogo operatora vtorogo poryadka”, Izv. vuzov. Matem., 2024, no. 7, 47–62
M. Yu. Vatolkin, “Investigation of the Dimension of the Spectral Projection of a Self-Adjoint Second-Order Quasidifferential Operator”, Russ Math., 68:7 (2024), 34
M. Yu. Vatolkin, “On the approximation of the first eigenvalue of some boundary value problems”, Comput. Math. Math. Phys., 64:6 (2024), 1224–1239
Michael Ruzhansky, Alibek Yeskermessuly, “Wave Equation for Sturm–Liouville Operator with Singular Intermediate Coefficient and Potential”, Bull. Malays. Math. Sci. Soc., 46:6 (2023)
Nilüfer TOPSAKAL, Rauf AMİROV, “On GLM type integral equation for singular Sturm-Liouville operator which has discontinuous coefficient”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 71:2 (2022), 305
Bondarenko N.P., “A Partial Inverse Sturm-Liouville Problem on An Arbitrary Graph”, Math. Meth. Appl. Sci., 44:8 (2021), 6896–6910
Bondarenko N.P., “Solving An Inverse Problem For the Sturm-Liouville Operator With Singular Potential By Yurko'S Method”, Tamkang J. Math., 52:1, SI (2021), 125–154
N. P. Bondarenko, “Direct and Inverse Problems for the Matrix Sturm–Liouville Operator with General Self-Adjoint Boundary Conditions”, Math. Notes, 109:3 (2021), 358–378
Aldana C.L. Caillau J.-B. Freitas P., “Maximal Determinants of Schrodinger Operators on Bounded Intervals”, J. Ecole Polytech.-Math., 7 (2020), 803–829
Yang Ch.-F., Bondarenko N.P., “A Partial Inverse Problem For the Sturm-Liouville Operator on the Lasso-Graph”, Inverse Probl. Imaging, 13:1 (2019), 69–79
Bondarenko N.P., “An Inverse Problem For Sturm-Liouville Operators on Trees With Partial Information Given on the Potentials”, Math. Meth. Appl. Sci., 42:5 (2019), 1512–1528
Guliyev N.J., “Schrodinger Operators With Distributional Potentials and Boundary Conditions Dependent on the Eigenvalue Parameter”, J. Math. Phys., 60:6 (2019), 063501
L. V. Kritskov, “Bessel property of the system of root functions of a second-order singular operator on an interval”, Differ. Equ., 54:8 (2018), 1032–1048
Leonid V. Kritskov, Springer Proceedings in Mathematics & Statistics, 216, Functional Analysis in Interdisciplinary Applications, 2017, 245
A. Yu. Trynin, “On inverse nodal problem for Sturm-Liouville operator”, Ufa Math. J., 5:4 (2013), 112–124

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

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