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Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri

Year 2022, Volume: 11 Issue: 3, 324 - 330, 31.12.2022

Hayati Olğar

Abstract

Fizik, mühendislik ve doğa bilimlerinin çeşitli dallarındaki birçok problemin çözümünde çeşitli tipte Sturm-Liouville problemleri karşımıza çıkmaktadır. Bu nedenle, diferansiyel operatörlerin spektral teorisinin temel kavramları ve yöntemleri; matematiksel fiziğin çeşitli problemlerinin Fourier yöntemiyle çözülmesi sonucu formüle edilmiş ve geliştirilmiştir. Son yıllarda, birçok fiziksel olgunun matematiksel bir modeli olmaları nedeniyle; yalnızca sınır koşulları değil, aynı zamanda geçiş şartları olarak da adlandırılan ilave sınır şartları içeren çok-aralıklı Sturm-Liouville problemlerine olan ilgide dikkate değer bir canlanma olmuştur. Bu çalışmanın amacı, klasik Sturm-Liouville problemlerinden farklı olarak Sturm-Liouville tipi yeni tipten çok aralıklı sınır değer problemini incelemektir. Bu çalışmada incelenen Sturm-Liouville tipi yeni tipten çok aralıklı sınır değer probleminin klasik sınır değer problemlerinden farklı olarak hem sınır şartlarının her ikisinde özdeğer parametresinin hem de geçiş şartları olarak bilinen dört ek etkileşim şartının bulunduğunu vurgulamak istedik.

Keywords

Sınır değer problemi sınır şartları geçiş şartları operator-polinom

References

  • Allahverdiev, B. P., Tuna, H. 2020. Eigenfunction expansion for singular Sturm–Liouville problems with transmission conditions. Electron. J. Differ. Equ. 3, 4286–4302.
  • Allahverdiev, B., Tuna, H. 2019. Eigenfunction expansion for singular sturm-liouville problems with transmission conditions. Electron. J. Differ. Equ. 3, 1–10.
  • Ao, J., Zhang, L. 2020. An inverse spectral problem of Sturm–Liouville problems with transmission conditions. Mediterr J Math., 17(5):1-24.
  • Atkinson, F. V. 1964. Discrete and Continuous Boundary Problems, Academic Press, New York.
  • Aydemir, K., Mukhtarov O. Sh. 2017. Class of Sturm-Liouville problems with eigenparameter dependent transmission conditions. Numer. Funct. Anal. 3rd Optim. 38(10), 1260–1275.
  • Bairamov, E., Aygar, Y. ve Oznur, G. B. 2019. Scattering properties of eigenparameter dependent impulsive Sturm–Liouville Equations. Bulletin of the Malaysian Mathematical Sciences Society, 4 2769-2781.
  • Belinskiy, B.P. ve Dauer, J.P. 1997. On a regular Sturm-Liouville problem on a finite interval with the eigenvalue parameter appearing linearly in the boundary conditions. Spectral theory and computational methods of Sturm-Liouville problem, Eds. D. Hinton and P. W. Schaefer, 1997.
  • Çavuşoğlu, S., Mukhtarov, O. S. 2021a. A new finite difference method for computing approximate solutions of boundary value problems including transition conditions. Вестник Карагандинского университета. Серия: Математика, (2), 54-61.
  • Çavuşoğlu, S., Mukhtarov, O. and Olğar, H. 2021b. Finite Difference Method for Approximate Solution of a Boundary Value Problem with Interior Singular Point. Konuralp Journal of Mathematics (KJM), vol. 9, no. 1, pp. 40-48.
  • Faydaoglu, S., Guseinov, G. Sh. 2010. An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics, 34 (3), 355-366.
  • Fulton, C. T. 1977. Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. R. Soc. Edinburgh, A77, 293-308.
  • Gohberg, I. C., Krein, M. G. 1969. Introduction to The Theory of Linear Non-Selfadjoint Operators, Translation of Mathematical Monographs, vol. 18, Amer. Math. Soc., Providence, Rhode Island.
  • Guliyev, Namig J. 2019. Schrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameter. J. Math. Phys. 60, no. 6, 063501, 23.
  • Hinton, D. B. 1979. An Expansion Theorem for an Eigenvalue Problem with Eigenvalue Parameter in the Boundary Conditions. Quart J. Math. Oxford (2), 33-42.
  • Ladyzhenskaia, O. A. 1985. The Boundary Value Problems Of Mathematical Physics, Springer-Verlag, New York.
  • Li, K., Wang, P. 2022. Properties for fourth order discontinuous differential operators with eigenparameter dependent boundary conditions, AIMS Mathematics, 7(6), 11487–11508.
  • Mukhtarov, O. S., Aydemir, K. 2021. Oscillation properties for non-classical Sturm-Liouville problems with additional transmission conditions. Mathematical Modelling and Analysis, 26(3), 432-443.
  • Mukhtarov, O. Sh, Olğar, H. ve Aydemir, K. 2015. Resolvent Operator and Spectrum of New Type Boundary Value Problems. Filomat 29, 1671–1680.
  • Mukhtarov, O. Sh., Olğar, H., Muhtarov, F.S., Aydemir, K. 2022. The Weak Eigenfunctions of Boundary-Value Problem with Symmetric Discontinuities, Journal of Applied Analysis 28(2), 275-283.
  • Mukhtarov, O.S., Yücel, M. 2020. A study of the eigenfunctions of the singular Sturm–Liouville problem using the analytical method and the decomposition technique. Mathematics 8, 415–429.
  • Mukhtarov, O. Sh., Yücel, M., Aydemir, K. 2020. Treatment a new approximation method and its justification for Sturm–Liouville problems. Complexity 5, 2020.
  • Olğar, H. 2019. Selfadjointness and Positiveness of the Differential Operators Generated by New Type Sturm-Liouville Problems, Cumhuriyet Sci. J. 40 (1), 24-34.
  • Stakgold I. 1971. Boudary Value Problems of Mathematical Physics, II, Macmillan Co., New York.
  • Şen, E., Açıkgöz, M., Aracı, S. 2017. Spectral problem for Sturm-Liouville operator with retarded argument which contains a spectral parameter in the boundary condition. Ukrainian Mathematical Journal 68,8, 1263-1277.
  • Tikhonov, A. N., Samarskii, A. A. 1963. Equations Of Mathematical Physics, Oxford and New York, Pergamon.
  • Titchmars, E. C. 1962. Eigenfunctions Expansion Associated with Second Order Differential Equations I, Second Edn. Oxford Univ. press, London.
  • Uğurlu, E., Bairamov, E. 2014. Spectral analysis of eigenparameter dependent boundary value transmission problems, Journal of Mathematical Analysis and Applications, 443(1), 482-494.
  • Walter, J. 1973. Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions. Math. Z., 133, 301-312.
  • Yakar, A., Akdogan, Z. 2017. On the fundamental solutions of a discontinuous fractional boundary value problem, Adv Differ Equ 2017; 378.
  • Zhang, M. Z., Wang, Y. C. 2015. Dependence of eigenvalues of Sturm-Liouville problems with interface conditions, Appl. Math. Comput. 265, 31-39.

Year 2022, Volume: 11 Issue: 3, 324 - 330, 31.12.2022

Hayati Olğar

Abstract

Keywords

Sınır değer problemi sınır şartları geçiş şartları operator-polinom

References

  • Allahverdiev, B. P., Tuna, H. 2020. Eigenfunction expansion for singular Sturm–Liouville problems with transmission conditions. Electron. J. Differ. Equ. 3, 4286–4302.
  • Allahverdiev, B., Tuna, H. 2019. Eigenfunction expansion for singular sturm-liouville problems with transmission conditions. Electron. J. Differ. Equ. 3, 1–10.
  • Ao, J., Zhang, L. 2020. An inverse spectral problem of Sturm–Liouville problems with transmission conditions. Mediterr J Math., 17(5):1-24.
  • Atkinson, F. V. 1964. Discrete and Continuous Boundary Problems, Academic Press, New York.
  • Aydemir, K., Mukhtarov O. Sh. 2017. Class of Sturm-Liouville problems with eigenparameter dependent transmission conditions. Numer. Funct. Anal. 3rd Optim. 38(10), 1260–1275.
  • Bairamov, E., Aygar, Y. ve Oznur, G. B. 2019. Scattering properties of eigenparameter dependent impulsive Sturm–Liouville Equations. Bulletin of the Malaysian Mathematical Sciences Society, 4 2769-2781.
  • Belinskiy, B.P. ve Dauer, J.P. 1997. On a regular Sturm-Liouville problem on a finite interval with the eigenvalue parameter appearing linearly in the boundary conditions. Spectral theory and computational methods of Sturm-Liouville problem, Eds. D. Hinton and P. W. Schaefer, 1997.
  • Çavuşoğlu, S., Mukhtarov, O. S. 2021a. A new finite difference method for computing approximate solutions of boundary value problems including transition conditions. Вестник Карагандинского университета. Серия: Математика, (2), 54-61.
  • Çavuşoğlu, S., Mukhtarov, O. and Olğar, H. 2021b. Finite Difference Method for Approximate Solution of a Boundary Value Problem with Interior Singular Point. Konuralp Journal of Mathematics (KJM), vol. 9, no. 1, pp. 40-48.
  • Faydaoglu, S., Guseinov, G. Sh. 2010. An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics, 34 (3), 355-366.
  • Fulton, C. T. 1977. Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. R. Soc. Edinburgh, A77, 293-308.
  • Gohberg, I. C., Krein, M. G. 1969. Introduction to The Theory of Linear Non-Selfadjoint Operators, Translation of Mathematical Monographs, vol. 18, Amer. Math. Soc., Providence, Rhode Island.
  • Guliyev, Namig J. 2019. Schrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameter. J. Math. Phys. 60, no. 6, 063501, 23.
  • Hinton, D. B. 1979. An Expansion Theorem for an Eigenvalue Problem with Eigenvalue Parameter in the Boundary Conditions. Quart J. Math. Oxford (2), 33-42.
  • Ladyzhenskaia, O. A. 1985. The Boundary Value Problems Of Mathematical Physics, Springer-Verlag, New York.
  • Li, K., Wang, P. 2022. Properties for fourth order discontinuous differential operators with eigenparameter dependent boundary conditions, AIMS Mathematics, 7(6), 11487–11508.
  • Mukhtarov, O. S., Aydemir, K. 2021. Oscillation properties for non-classical Sturm-Liouville problems with additional transmission conditions. Mathematical Modelling and Analysis, 26(3), 432-443.
  • Mukhtarov, O. Sh, Olğar, H. ve Aydemir, K. 2015. Resolvent Operator and Spectrum of New Type Boundary Value Problems. Filomat 29, 1671–1680.
  • Mukhtarov, O. Sh., Olğar, H., Muhtarov, F.S., Aydemir, K. 2022. The Weak Eigenfunctions of Boundary-Value Problem with Symmetric Discontinuities, Journal of Applied Analysis 28(2), 275-283.
  • Mukhtarov, O.S., Yücel, M. 2020. A study of the eigenfunctions of the singular Sturm–Liouville problem using the analytical method and the decomposition technique. Mathematics 8, 415–429.
  • Mukhtarov, O. Sh., Yücel, M., Aydemir, K. 2020. Treatment a new approximation method and its justification for Sturm–Liouville problems. Complexity 5, 2020.
  • Olğar, H. 2019. Selfadjointness and Positiveness of the Differential Operators Generated by New Type Sturm-Liouville Problems, Cumhuriyet Sci. J. 40 (1), 24-34.
  • Stakgold I. 1971. Boudary Value Problems of Mathematical Physics, II, Macmillan Co., New York.
  • Şen, E., Açıkgöz, M., Aracı, S. 2017. Spectral problem for Sturm-Liouville operator with retarded argument which contains a spectral parameter in the boundary condition. Ukrainian Mathematical Journal 68,8, 1263-1277.
  • Tikhonov, A. N., Samarskii, A. A. 1963. Equations Of Mathematical Physics, Oxford and New York, Pergamon.
  • Titchmars, E. C. 1962. Eigenfunctions Expansion Associated with Second Order Differential Equations I, Second Edn. Oxford Univ. press, London.
  • Uğurlu, E., Bairamov, E. 2014. Spectral analysis of eigenparameter dependent boundary value transmission problems, Journal of Mathematical Analysis and Applications, 443(1), 482-494.
  • Walter, J. 1973. Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions. Math. Z., 133, 301-312.
  • Yakar, A., Akdogan, Z. 2017. On the fundamental solutions of a discontinuous fractional boundary value problem, Adv Differ Equ 2017; 378.
  • Zhang, M. Z., Wang, Y. C. 2015. Dependence of eigenvalues of Sturm-Liouville problems with interface conditions, Appl. Math. Comput. 265, 31-39.
There are 30 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Araştırma Makaleleri
Authors

Hayati Olğar

Early Pub Date December 30, 2022
Publication Date December 31, 2022
Published in Issue Year 2022 Volume: 11 Issue: 3

Cite

APA Olğar, H. (2022). Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri. Gaziosmanpaşa Bilimsel Araştırma Dergisi, 11(3), 324-330.
AMA Olğar H. Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri. GBAD. December 2022;11(3):324-330.
Chicago Olğar, Hayati. “Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri”. Gaziosmanpaşa Bilimsel Araştırma Dergisi 11, no. 3 (December 2022): 324-30.
EndNote Olğar H (December 1, 2022) Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri. Gaziosmanpaşa Bilimsel Araştırma Dergisi 11 3 324–330.
IEEE H. Olğar, “Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri”, GBAD, vol. 11, no. 3, pp. 324–330, 2022.
ISNAD Olğar, Hayati. “Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri”. Gaziosmanpaşa Bilimsel Araştırma Dergisi 11/3 (December 2022), 324-330.
JAMA Olğar H. Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri. GBAD. 2022;11:324–330.
MLA Olğar, Hayati. “Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri”. Gaziosmanpaşa Bilimsel Araştırma Dergisi, vol. 11, no. 3, 2022, pp. 324-30.
Vancouver Olğar H. Çok Aralıklı Bir Sınır Değer Probleminin Bazı Spektral Özellikleri. GBAD. 2022;11(3):324-30.
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