O. Sh. Mukhtarov, M. Kadakal, “Some spectral properties of one Sturm–Liouville type problem with discontinuous weight”, Sibirsk. Mat. Zh., 46:4 (2005), 860–875; Siberian Math. J., 46:4 (2005), 681

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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 4, Pages 860–875 (Mi smj1010)

This article is cited in 41 scientific papers (total in 41 papers)

Some spectral properties of one Sturm–Liouville type problem with discontinuous weight

O. Sh. Mukhtarov^a, M. Kadakal^b

^a Gaziosmanpasha University
^b Ondokuz Mayis University

Full-text PDF (246 kB) Citations (41)

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Abstract: We consider a discontinuous weight Sturm–Liouville equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at the point of discontinuity. We extend and generalize some approaches and results of the classic regular Sturm–Liouville problems to the similar problems with discontinuities. In particular, we introduce a special Hilbert space formulation in such a way that the problem under consideration can be interpreted as an eigenvalue problem for a suitable selfadjoint operator, construct the Green's function and resolvent operator, and derive asymptotic formulas for eigenvalues and normalized eigenfunctions.

Keywords: discontinuous Sturm–Liouville problems, transmission conditions, eigenvalues, eigenfunctions, Green?s function, resolvent.

Received: 29.07.2004

English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 4, Pages 681–694
DOI: https://doi.org/10.1007/s11202-005-0069-z

Bibliographic databases:

UDC: 517.927

Language: Russian

Citation: O. Sh. Mukhtarov, M. Kadakal, “Some spectral properties of one Sturm–Liouville type problem with discontinuous weight”, Sibirsk. Mat. Zh., 46:4 (2005), 860–875; Siberian Math. J., 46:4 (2005), 681–694

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj1010

https://www.mathnet.ru/eng/smj/v46/i4/p860

This publication is cited in the following 41 articles:

慧洁付, “Second-Order <i>J</i>-Symmetric Differential Operators with Eigenparameter-Dependent Boundary and Transmission Conditions”, AAM, 14:01 (2025), 374
Zheng Zhaowen, Li Kun, Zhi Yunfang, “Inverse spectral problems of the non-selfadjoint discontinuous Sturm-Liouville operator with boundary conditions dependent on spectral parameters”, Sci. Sin.-Math., 2024
M. Yu. Vatolkin, “On the spectrum of a quasidifferential boundary value problem of the second order”, Russian Math. (Iz. VUZ), 67:1 (2023), 1–19
Dmitrii V. Antonov, Elena A. Shchepakina, Vladimir A. Sobolev, Sergey Y. Misyura, Igor G. Donskoy, Pavel A. Strizhak, Sergei S. Sazhin, “Dissociation of methane from a layer of methane-hydrate particles: A new simple model”, International Journal of Heat and Mass Transfer, 213 (2023), 124225
Qiuhong Lin, “Dependence of Eigenvalues of $(2n + 1)$ th Order Boundary Value Problems with Transmission Conditions”, J Nonlinear Math Phys, 30:3 (2023), 1190
Kun Li, Peng Wang, “Properties for fourth order discontinuous differential operators with eigenparameter dependent boundary conditions”, MATH, 7:6 (2022), 11487
V. P. Tanana, “Polnota sistemy sobstvennykh funktsii zadachi Shturma–Liuvillya s osobennostyu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:1 (2020), 59–63
Allahverdiev B.P., Tuna H., “on the Resolvent of Singular Sturm-Liouville Operators With Transmission Conditions”, Math. Meth. Appl. Sci., 43:7 (2020), 4286–4302
Volkan Ala, Khanlar R. Mamedov, “On Basis Property of Root Functions For a Class Second Order Differential Operator”, Applied Mathematics and Nonlinear Sciences, 5:1 (2020), 361
Allahverdiev B.P., Tuna H., “Eigenfunction Expansion For Singular Sturm-Liouville Problems With Transmission Conditions”, Electron. J. Differ. Equ., 2019, 03
Allahverdiev B.P., Tuna H., “a Spectral Theory For Discontinuous Sturm-Liouville Problems on the Whole Line”, Matematiche, 74:2 (2019), 235–251
Allahverdiev B.P., Tuna H., “Resolvent Operator of Singular Dirac System With Transmission Conditions”, Rad Hrvat. Akad. Znan. Umjet., 23:538 (2019), 85–105
Pasaoglu Allahverdiev B., Tuna H., “Spectral Expansion For the Singular Dirac System With Impulsive Conditions”, Turk. J. Math., 42:5 (2018), 2527–2545
Aydemir K., Olgar H., Mukhtarov O.Sh., Muhtarov F., “Differential Operator Equations With Interface Conditions in Modified Direct Sum Spaces”, Filomat, 32:3 (2018), 921–931
S. I. Mitrokhin, “Ob izuchenii spektralnykh svoistv differentsialnykh operatorov chetnogo poryadka s razryvnoi vesovoi funktsiei”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:121 (2018), 74–99
Olgar H., Mukhtarov O.Sh., “Weak Eigenfunctions of Two-Interval Sturm-Liouville Problems Together With Interaction Conditions”, J. Math. Phys., 58:4 (2017), 042201
Cai J., Zheng Zh., “a Singular Sturm-Liouville Problem With Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions”, Discrete Dyn. Nat. Soc., 2017, 9673846
S. I. Mitrokhin, “Study of differential operator with summable potential and discontinuous weight function”, Ufa Math. J., 9:4 (2017), 72–84
Aydemir K., Mukhtarov O.Sh., “Class of Sturm-Liouville Problems With Eigenparameter Dependent Transmission Conditions”, Numer. Funct. Anal. Optim., 38:10 (2017), 1260–1275
Aydemir K., Mukhtarov O.S.H., “Asymptotic Distribution of Eigenvalues and Eigenfunctions For a Multi-Point Discontinuous Sturm-Liouville Problem”, Electron. J. Differ. Equ., 2016, 131

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

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