Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, , 1 - 8, 30.04.2023
https://doi.org/10.54187/jnrs.1201577

Öz

Kaynakça

  • W. Magnus, S. Winkler. Hill's equation. Courier Corporation, 2013.
  • M. S. P. Eastham, The spectral theory of periodic differential equations, Scottish Academic Press, London, 1973.
  • B. M. Levitan, I. S. Sargsian. Introduction to spectral theory: Self-adjoint ordinary differential operators, American Mathematical Society, Volume 39, 1975.
  • E. C. Titchmarsh, Eigenfunctions expansion associated with second order differential equations I, 2nd edition, Oxford University Press, London, 1962.
  • A. Zettl, Sturm Liouville theory, American Mathematical Society, Volume 121, 2012.
  • O. Sh. Mukhtarov, S. Çavuşoğlu, P. K. Pandey, Development of the finite difference method to solve a new type Sturm-Liouville problems, Tbilisi Mathematical Journal 14 (3) (2021) 141-154.
  • O. Sh. Mukhtarov, M. Yücel, K. Aydemir, Treatment a new approximation method and its justification for Sturm-Liouville problems, Complexity 2020 (2020) Article ID 8019460 8 pages.
  • A. Yakar, Z. Akdoğan, n the fundamental solutions of a discontinuous fractional boundary value problem, Advances in Difference Equations 2017 (1) (2017) 1-15.
  • Z. Akdoğan, A. Yakar, M. Demirci, Discontinuous fractional Sturm-Liouville problems with transmission conditions, Applied Mathematics and Computation 350 (2019) 1-10.
  • B. P. Allahverdiev, E. Bairamov and E. Uğurlu, Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions, Journal of Mathematical Analysis and Applications 401 (1) (2013) 388-396.
  • B. P. Allahverdiev, H. Tuna, Eigenfunction expansion for singular Sturm-Liouville problems with transmission conditions, Electronic Journal of Differential Equations 2019 (3) (2019) 1-10.
  • B. P. Allahverdiev, H. Tuna, Discontinuous matrix Sturm-Liouville problems, Eurasian Mathematical Journal 13 (3) (2022) 8-22.
  • K. Aydemir, H. Olğar, O. Sh. Mukhtarov, F. S. Muhtarov, Differential operator equations with interface conditions in modified direct sum spaces, Filomat 32 (3) (2018) 921-931.
  • A. Cabada, J. A. Cid, On a class of singular Sturm-Liouville periodic boundary value problems, Nonlinear Analysis: Real World Applications 12 (4) (2011) 2378-2384.
  • F. S. Muhtarov, K. Aydemir, Distributions of eigenvalues for Sturm-Liouville problem under jump conditions, Journal of New Results in Science 1 (1) (2012) 81-89.
  • O. Sh. Mukhtarov, K. Aydemir, Spectral analysis of $\alpha$ semi periodic 2-interval Sturm-Liouville problems, Qualitative Theory of Dynamical Systems 21 (3) (2022) 1-14.
  • H. Olğar, O. Sh. Mukhtarov, K. Aydemir, Some properties of eigenvalues and generalized eigenvectors of one boundary value problem, Filomat 32 (3) (2018) 911-920.
  • H. Olğar, O. Sh. Mukhtarov, Weak eigenfunctions of two-interval Sturm-Liouville problems together with interaction conditions, Journal of Mathematical Physics 58 (4) (2017) 1-13.
  • H. Olğar, Selfadjointness and positiveness of the differential operators generated by new type Sturm-Liouville problems, Cumhuriyet Science Journal 40 (1) (2019) 24-34.
  • E. Şen, Computation of eigenvalues and eigenfunctions of a Schrodinger-type boundary-value-transmission problem with retarded argument, Mathematical Methods in the Applied Sciences 41 (16) (2018) 6604-6610.
  • E. Uğurlu, Investigation of the eigenvalues and root functions of the boundary value problem together with a transmission matrix, Quaestiones Mathematicae 43 (4) (2020) 507-521.

Non-classical periodic boundary value problems with impulsive conditions

Yıl 2023, , 1 - 8, 30.04.2023
https://doi.org/10.54187/jnrs.1201577

Öz

This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end (such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.). At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

Kaynakça

  • W. Magnus, S. Winkler. Hill's equation. Courier Corporation, 2013.
  • M. S. P. Eastham, The spectral theory of periodic differential equations, Scottish Academic Press, London, 1973.
  • B. M. Levitan, I. S. Sargsian. Introduction to spectral theory: Self-adjoint ordinary differential operators, American Mathematical Society, Volume 39, 1975.
  • E. C. Titchmarsh, Eigenfunctions expansion associated with second order differential equations I, 2nd edition, Oxford University Press, London, 1962.
  • A. Zettl, Sturm Liouville theory, American Mathematical Society, Volume 121, 2012.
  • O. Sh. Mukhtarov, S. Çavuşoğlu, P. K. Pandey, Development of the finite difference method to solve a new type Sturm-Liouville problems, Tbilisi Mathematical Journal 14 (3) (2021) 141-154.
  • O. Sh. Mukhtarov, M. Yücel, K. Aydemir, Treatment a new approximation method and its justification for Sturm-Liouville problems, Complexity 2020 (2020) Article ID 8019460 8 pages.
  • A. Yakar, Z. Akdoğan, n the fundamental solutions of a discontinuous fractional boundary value problem, Advances in Difference Equations 2017 (1) (2017) 1-15.
  • Z. Akdoğan, A. Yakar, M. Demirci, Discontinuous fractional Sturm-Liouville problems with transmission conditions, Applied Mathematics and Computation 350 (2019) 1-10.
  • B. P. Allahverdiev, E. Bairamov and E. Uğurlu, Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions, Journal of Mathematical Analysis and Applications 401 (1) (2013) 388-396.
  • B. P. Allahverdiev, H. Tuna, Eigenfunction expansion for singular Sturm-Liouville problems with transmission conditions, Electronic Journal of Differential Equations 2019 (3) (2019) 1-10.
  • B. P. Allahverdiev, H. Tuna, Discontinuous matrix Sturm-Liouville problems, Eurasian Mathematical Journal 13 (3) (2022) 8-22.
  • K. Aydemir, H. Olğar, O. Sh. Mukhtarov, F. S. Muhtarov, Differential operator equations with interface conditions in modified direct sum spaces, Filomat 32 (3) (2018) 921-931.
  • A. Cabada, J. A. Cid, On a class of singular Sturm-Liouville periodic boundary value problems, Nonlinear Analysis: Real World Applications 12 (4) (2011) 2378-2384.
  • F. S. Muhtarov, K. Aydemir, Distributions of eigenvalues for Sturm-Liouville problem under jump conditions, Journal of New Results in Science 1 (1) (2012) 81-89.
  • O. Sh. Mukhtarov, K. Aydemir, Spectral analysis of $\alpha$ semi periodic 2-interval Sturm-Liouville problems, Qualitative Theory of Dynamical Systems 21 (3) (2022) 1-14.
  • H. Olğar, O. Sh. Mukhtarov, K. Aydemir, Some properties of eigenvalues and generalized eigenvectors of one boundary value problem, Filomat 32 (3) (2018) 911-920.
  • H. Olğar, O. Sh. Mukhtarov, Weak eigenfunctions of two-interval Sturm-Liouville problems together with interaction conditions, Journal of Mathematical Physics 58 (4) (2017) 1-13.
  • H. Olğar, Selfadjointness and positiveness of the differential operators generated by new type Sturm-Liouville problems, Cumhuriyet Science Journal 40 (1) (2019) 24-34.
  • E. Şen, Computation of eigenvalues and eigenfunctions of a Schrodinger-type boundary-value-transmission problem with retarded argument, Mathematical Methods in the Applied Sciences 41 (16) (2018) 6604-6610.
  • E. Uğurlu, Investigation of the eigenvalues and root functions of the boundary value problem together with a transmission matrix, Quaestiones Mathematicae 43 (4) (2020) 507-521.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Sevda Nur Öztürk 0000-0001-5722-3393

Oktay Mukhtarov 0000-0001-7480-6857

Kadriye Aydemir 0000-0002-8378-3949

Yayımlanma Tarihi 30 Nisan 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Öztürk, S. N., Mukhtarov, O., & Aydemir, K. (2023). Non-classical periodic boundary value problems with impulsive conditions. Journal of New Results in Science, 12(1), 1-8. https://doi.org/10.54187/jnrs.1201577
AMA Öztürk SN, Mukhtarov O, Aydemir K. Non-classical periodic boundary value problems with impulsive conditions. JNRS. Nisan 2023;12(1):1-8. doi:10.54187/jnrs.1201577
Chicago Öztürk, Sevda Nur, Oktay Mukhtarov, ve Kadriye Aydemir. “Non-Classical Periodic Boundary Value Problems With Impulsive Conditions”. Journal of New Results in Science 12, sy. 1 (Nisan 2023): 1-8. https://doi.org/10.54187/jnrs.1201577.
EndNote Öztürk SN, Mukhtarov O, Aydemir K (01 Nisan 2023) Non-classical periodic boundary value problems with impulsive conditions. Journal of New Results in Science 12 1 1–8.
IEEE S. N. Öztürk, O. Mukhtarov, ve K. Aydemir, “Non-classical periodic boundary value problems with impulsive conditions”, JNRS, c. 12, sy. 1, ss. 1–8, 2023, doi: 10.54187/jnrs.1201577.
ISNAD Öztürk, Sevda Nur vd. “Non-Classical Periodic Boundary Value Problems With Impulsive Conditions”. Journal of New Results in Science 12/1 (Nisan 2023), 1-8. https://doi.org/10.54187/jnrs.1201577.
JAMA Öztürk SN, Mukhtarov O, Aydemir K. Non-classical periodic boundary value problems with impulsive conditions. JNRS. 2023;12:1–8.
MLA Öztürk, Sevda Nur vd. “Non-Classical Periodic Boundary Value Problems With Impulsive Conditions”. Journal of New Results in Science, c. 12, sy. 1, 2023, ss. 1-8, doi:10.54187/jnrs.1201577.
Vancouver Öztürk SN, Mukhtarov O, Aydemir K. Non-classical periodic boundary value problems with impulsive conditions. JNRS. 2023;12(1):1-8.


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