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Spectral Properties of Discontinuous Boundary Value Problem with Transmission Conditions and Manypoint Singularities

Year 2023, , 258 - 269, 31.12.2023
https://doi.org/10.47000/tjmcs.1138229

Abstract

In this study, we investigate a discontinuous Sturm-Liouville boundary value problem on three intervals
with manypoint-transmission conditions in direct sum of Sobolev space. We establish such spectral properties as Fredholmness and coreciveness with respect to the eigenvalue parameter

References

  • Agranovich, M.S., Spectral properties of diffraction problems The Generalized Method of Eigenoscillations in the Theory of Diffraction Theory, 1977 (in Russian: translated into English Wiley-VCH, Berlin), 1999.
  • Akdoğan, Z., Yakar, A., Demirci, M., Discontinuous fractional Sturm-Liouville problems with transmission conditions, Applied Mathematics and Computation, , 350(2019), 1–10.
  • Aliyev, Z.S., Basis properties of a fourth order differential operator with spectral parameter in the boundary condition, Open Mathematics, 8(2)(2010), 378–388.
  • Aydemir, K., Boundary value problems with eigenvalue depending boundary and transmission conditions, Boundary Value Problems, 131(2014).
  • Aydemir, K., Mukhtarov, O.Sh. Spectrum and Green’s function of a many-interval Sturm-Liouville problem, Z. Naturforsch., 70(5)(2015), 301–308.
  • Besow, O.V., Il’in, V.P., Nikolskii, S.M., Integral Pepresentation of Functional and Embedding Theorems, 1, State New York, 1978.
  • Borsuk, M., Transmission Problems for Elliptic Second-order Equations in Non-smooth Domains, Springer, Basel AG, 2010.
  • Garcia-Huidobra, M., Gupta Chaitan, P., Manasevich, R., Some multipoint boundary value problems of Neumann-Dirichlet type involving a multipoint p-Laplace like operator, J. Math. Anal. Appl., 333(2007), 247–264.
  • Imanbaev, N.S., Kanguzhin, B.E., Kalimbetov, B.T., On zeros of the characteristic determinant ofthe spectral problem for a third-order differential operator on a segment with nonlocal boundary conditions, Advances in Difference Equations, 110(2013).
  • Kandemir, M., Mukhtarov, O. Sh., Yakubov, Ya. Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter, Mediterranean Journal of Mathematics, 6(2009), 317–338.
  • Kandemir, M., Yakubov, Ya., Regular boundary value problems with a discontinuous coefficient, functional-multipoint conditions, and a linear spectral parameter, Israel Journal of Mathematics, 180(2010), 255–270.
  • Kandemir, M., Irregular boundary value problems for elliptic differential-operator equations with discontinuous coefficients and transmission conditions, Kuwait Journal of Science and Engineering, 39(1A)(2012), 71–97.
  • Kandemir, M., Mukhtarov, O. Sh., Nonlocal Sturm-Liouville problems with integral terms in the boundary condıtıons, Electronic Journal of Differential Equations, 11(2017), 1–12.
  • Kandemir, M., Mukhtarov, O. Sh., Manypoint boundary value problems for elliptic differential-operator equations with interior singularities, Mediterr. J. Math., (2020), 17–35.
  • Kato, T., Perturbation Theory for Linear Operators, Sipringer-Verlag, New York Inc., 1966.
  • Likov, A.V., Mikhailov, Yu. A., The Theory of Heat and Mass Transfer, Qosenergaizdat, (Russian), 1963.
  • Margareth, S.A., Rivera, J.E., Mauricio, S., Villagran, O.V., Transmission problem in thermoelasticity, Hindawi Pub. Cor. B.V.P., ID 190548(2011), 33.
  • Mukhtarov, O. Sh., Discontinuous boundary value problem with spectral parameter in boundary conditions, Turkish J. Math., 18(2)(1994), 183–192.
  • Mukhtarov, O. Sh., Yakubov, S., Problems for ordinary differential equations with transmission conditions, Applicable Analysis, 81(2002), 1033–1064.
  • Mukhtarov, O. Sh., Aydemir, K., Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, Acta Mathematica Scienta, 35B(3)(2015), 639–649.
  • Rasulov, M.L., Application of Contour Integral Method, (in Russian), Navka, Moskow, 1997.
  • Sadybekov, M.A., Turmetov, B. Kh., Solvability of nonlocal boundary-value problems for the Laplace equatıon in the ball, Electronic Journal of Differential Equations, 157(2014), 1–14.
  • Shakhmurov, V.B., Linear and nonlinear abstract elliptic equations with VMO coefficients and applications, Fixed point theory and applications, 6(2013), 1–21.
  • Titeux, I., Yakubov, Ya., Completeness of root functions for thermal conduction in a strip with piecewise continuous coefficients, Math. Models and Methods in Applied Sciences, 7(1997), 1035–1050.
  • Triebel, H., Interpolation Theory Function Spaces, Differential Operators, North Holland, Amsterdam, 1978.
  • Voitovich, N.N., Katsenelbaum, B.Z., Sivov, A., Generalized Method of Eigen-vibration in the Theory of Diffraction, (Russian), Nauka, Moscow, 1997.
  • Yakar, A., Akdoğan, Z., On the fundamental solutions of a discontinuous fractional boundary value problem, Adv. Differ. Equ., 378(2017).
  • Yakubov, S., Yakubov, Ya., Differential-operator Equation Ordinary and Partial Differential Equation, Chapman and Hall/CRC, Boca Raton, London State New York Washington, State D. C., 1999.
Year 2023, , 258 - 269, 31.12.2023
https://doi.org/10.47000/tjmcs.1138229

Abstract

References

  • Agranovich, M.S., Spectral properties of diffraction problems The Generalized Method of Eigenoscillations in the Theory of Diffraction Theory, 1977 (in Russian: translated into English Wiley-VCH, Berlin), 1999.
  • Akdoğan, Z., Yakar, A., Demirci, M., Discontinuous fractional Sturm-Liouville problems with transmission conditions, Applied Mathematics and Computation, , 350(2019), 1–10.
  • Aliyev, Z.S., Basis properties of a fourth order differential operator with spectral parameter in the boundary condition, Open Mathematics, 8(2)(2010), 378–388.
  • Aydemir, K., Boundary value problems with eigenvalue depending boundary and transmission conditions, Boundary Value Problems, 131(2014).
  • Aydemir, K., Mukhtarov, O.Sh. Spectrum and Green’s function of a many-interval Sturm-Liouville problem, Z. Naturforsch., 70(5)(2015), 301–308.
  • Besow, O.V., Il’in, V.P., Nikolskii, S.M., Integral Pepresentation of Functional and Embedding Theorems, 1, State New York, 1978.
  • Borsuk, M., Transmission Problems for Elliptic Second-order Equations in Non-smooth Domains, Springer, Basel AG, 2010.
  • Garcia-Huidobra, M., Gupta Chaitan, P., Manasevich, R., Some multipoint boundary value problems of Neumann-Dirichlet type involving a multipoint p-Laplace like operator, J. Math. Anal. Appl., 333(2007), 247–264.
  • Imanbaev, N.S., Kanguzhin, B.E., Kalimbetov, B.T., On zeros of the characteristic determinant ofthe spectral problem for a third-order differential operator on a segment with nonlocal boundary conditions, Advances in Difference Equations, 110(2013).
  • Kandemir, M., Mukhtarov, O. Sh., Yakubov, Ya. Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter, Mediterranean Journal of Mathematics, 6(2009), 317–338.
  • Kandemir, M., Yakubov, Ya., Regular boundary value problems with a discontinuous coefficient, functional-multipoint conditions, and a linear spectral parameter, Israel Journal of Mathematics, 180(2010), 255–270.
  • Kandemir, M., Irregular boundary value problems for elliptic differential-operator equations with discontinuous coefficients and transmission conditions, Kuwait Journal of Science and Engineering, 39(1A)(2012), 71–97.
  • Kandemir, M., Mukhtarov, O. Sh., Nonlocal Sturm-Liouville problems with integral terms in the boundary condıtıons, Electronic Journal of Differential Equations, 11(2017), 1–12.
  • Kandemir, M., Mukhtarov, O. Sh., Manypoint boundary value problems for elliptic differential-operator equations with interior singularities, Mediterr. J. Math., (2020), 17–35.
  • Kato, T., Perturbation Theory for Linear Operators, Sipringer-Verlag, New York Inc., 1966.
  • Likov, A.V., Mikhailov, Yu. A., The Theory of Heat and Mass Transfer, Qosenergaizdat, (Russian), 1963.
  • Margareth, S.A., Rivera, J.E., Mauricio, S., Villagran, O.V., Transmission problem in thermoelasticity, Hindawi Pub. Cor. B.V.P., ID 190548(2011), 33.
  • Mukhtarov, O. Sh., Discontinuous boundary value problem with spectral parameter in boundary conditions, Turkish J. Math., 18(2)(1994), 183–192.
  • Mukhtarov, O. Sh., Yakubov, S., Problems for ordinary differential equations with transmission conditions, Applicable Analysis, 81(2002), 1033–1064.
  • Mukhtarov, O. Sh., Aydemir, K., Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, Acta Mathematica Scienta, 35B(3)(2015), 639–649.
  • Rasulov, M.L., Application of Contour Integral Method, (in Russian), Navka, Moskow, 1997.
  • Sadybekov, M.A., Turmetov, B. Kh., Solvability of nonlocal boundary-value problems for the Laplace equatıon in the ball, Electronic Journal of Differential Equations, 157(2014), 1–14.
  • Shakhmurov, V.B., Linear and nonlinear abstract elliptic equations with VMO coefficients and applications, Fixed point theory and applications, 6(2013), 1–21.
  • Titeux, I., Yakubov, Ya., Completeness of root functions for thermal conduction in a strip with piecewise continuous coefficients, Math. Models and Methods in Applied Sciences, 7(1997), 1035–1050.
  • Triebel, H., Interpolation Theory Function Spaces, Differential Operators, North Holland, Amsterdam, 1978.
  • Voitovich, N.N., Katsenelbaum, B.Z., Sivov, A., Generalized Method of Eigen-vibration in the Theory of Diffraction, (Russian), Nauka, Moscow, 1997.
  • Yakar, A., Akdoğan, Z., On the fundamental solutions of a discontinuous fractional boundary value problem, Adv. Differ. Equ., 378(2017).
  • Yakubov, S., Yakubov, Ya., Differential-operator Equation Ordinary and Partial Differential Equation, Chapman and Hall/CRC, Boca Raton, London State New York Washington, State D. C., 1999.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Tevhide Baltürk 0000-0001-5276-6698

Mustafa Kandemir 0000-0003-3212-8976

Publication Date December 31, 2023
Published in Issue Year 2023

Cite

APA Baltürk, T., & Kandemir, M. (2023). Spectral Properties of Discontinuous Boundary Value Problem with Transmission Conditions and Manypoint Singularities. Turkish Journal of Mathematics and Computer Science, 15(2), 258-269. https://doi.org/10.47000/tjmcs.1138229
AMA Baltürk T, Kandemir M. Spectral Properties of Discontinuous Boundary Value Problem with Transmission Conditions and Manypoint Singularities. TJMCS. December 2023;15(2):258-269. doi:10.47000/tjmcs.1138229
Chicago Baltürk, Tevhide, and Mustafa Kandemir. “Spectral Properties of Discontinuous Boundary Value Problem With Transmission Conditions and Manypoint Singularities”. Turkish Journal of Mathematics and Computer Science 15, no. 2 (December 2023): 258-69. https://doi.org/10.47000/tjmcs.1138229.
EndNote Baltürk T, Kandemir M (December 1, 2023) Spectral Properties of Discontinuous Boundary Value Problem with Transmission Conditions and Manypoint Singularities. Turkish Journal of Mathematics and Computer Science 15 2 258–269.
IEEE T. Baltürk and M. Kandemir, “Spectral Properties of Discontinuous Boundary Value Problem with Transmission Conditions and Manypoint Singularities”, TJMCS, vol. 15, no. 2, pp. 258–269, 2023, doi: 10.47000/tjmcs.1138229.
ISNAD Baltürk, Tevhide - Kandemir, Mustafa. “Spectral Properties of Discontinuous Boundary Value Problem With Transmission Conditions and Manypoint Singularities”. Turkish Journal of Mathematics and Computer Science 15/2 (December 2023), 258-269. https://doi.org/10.47000/tjmcs.1138229.
JAMA Baltürk T, Kandemir M. Spectral Properties of Discontinuous Boundary Value Problem with Transmission Conditions and Manypoint Singularities. TJMCS. 2023;15:258–269.
MLA Baltürk, Tevhide and Mustafa Kandemir. “Spectral Properties of Discontinuous Boundary Value Problem With Transmission Conditions and Manypoint Singularities”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 2, 2023, pp. 258-69, doi:10.47000/tjmcs.1138229.
Vancouver Baltürk T, Kandemir M. Spectral Properties of Discontinuous Boundary Value Problem with Transmission Conditions and Manypoint Singularities. TJMCS. 2023;15(2):258-69.