Research Article
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Year 2020, Issue: 33, 40 - 49, 31.12.2020

Serdar Paş Kadriye Aydemir Fahreddin Muhtarov

Abstract

Supporting Institution

Amasya Üniversitesi

Project Number

FMB-BAP 19-0391.

References

  • [1] G. D. Birkhoff, On the Asymptotic Character of the Solution of the Certain Linear Differential Equations (1908).
  • [2] J. D. Tamarkin, Some General Problems of The Theory of Ordinary Linear Differential Equations And Expansions of An Arbitary Function in Series of Fundamental Functions, Math. Z. 27 (1928) 1-54.
  • [3] J. W. Lee, Spectral Properties and Oscillation Theorems for Periodic Boundary-Value Problems of Sturm Liouville Type, Journal of Differential Equations 11 (1972) 592-606.
  • [4] G. V. Berghe, M. V. Daele, H. D. Meyer, A modified difference scheme for periodic and semiperiodic Sturm-Liouville problems, Applied Numerical Mathematics 18 (1995) 69-78.
  • [5] Y. Liu, Periodic Boundary Value Problems for Higher Order Impulsive Functional Differential Equations. SDÜ Fen Edebiyat Fakültesi Fen Dergisi (E-dergi) 2 (2007) 253-272.
  • [6] D. B. Wang, Periodic Boundary Value Problems for Nonlinear First-Order Impulsive Dynamic Equations on Time Scales, Advances in Difference Equations 12 (2012).
  • [7] V. Malathi, B. S. Mohamed, B. T. Bachok, Computing Eigenvalues Of Periodic Sturm-Liouville Problems Using Shooting Technique And Direct Integration Method, International Journal of Computer Mathematics, 68 (1996) 119-132.
  • [8] K. Aydemir, O. Sh. Mukhtarov, Completeness Of One Two-Interval Boundary Value Problem With Transmission Conditions, Miskolc Mathematical Notes 15 (2014) 293-303.
  • [9] K. Aydemir, O. Sh. Mukhtarov, Class of Sturm-Liouville problems with eigen-parameter dependent transmission conditions, Numerical Functional Analysis and Optimization 38(10) (2017) 1260-1275.
  • [10] M. Kandemir, O. Sh. Mukhtarov, Nonlocal Sturm-Liouville problems with integral terms in the boundary conditions, Electronic Journal of Differential Equations 11 (2017) 112.
  • [11] O. Sh. Mukhtarov, H. Olğar, K. Aydemir, Resolvent Operator and Spectrum of New Type Boundary Value Problems, Filomat 29 (2015) 1671–1680.
  • [12] O. Sh. Mukhtarov, H. Olğar, K. Aydemir, I. Jabbarov, Operator-Pencil Realization Of One Sturm- Liouville Problem With Transmission Conditions, Applied And Computational Mathematics 17(2)(2018) 284-294.
  • [13] E. C. Titchmars, Eigenfunctions Expansion Associated with Second Order Differential Equations I, second edn. Oxford Univ. press, London 1962.

Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems

Year 2020, Issue: 33, 40 - 49, 31.12.2020

Serdar Paş Kadriye Aydemir Fahreddin Muhtarov

Abstract

This work is concerned with the boundary-value-transition problem consisting of a
two-interval Sturm-Liouville equation
Lu ≔ −u′′(x) + q(x)u(x) = λu(x) , x ∈ [−1,0) ∪ (0,1]

together with anti-periodic boundary conditions, given by
u(−1) = −u(1)
u′(−1) = −u′(1)
and transition conditions at the interior point x = 0, given by
u(+0) = Ku(−0)
u′(+0) =1/Ku′(−0)

where q(x) is a continuous function in the intervals [−1,0) and (0,1] with finite limit values q(±0) ,
K ≠ 0 is the real number and λ is the complex eigenvalue parameter. In this study we shall investigate
some properties of the eigenvalues and eigenfunctions of the considered problem.

Keywords

Anti-periodic Sturm-Liouville problem, eigenvalue, eigenfunction, transition condition

Project Number

FMB-BAP 19-0391.

References

  • [1] G. D. Birkhoff, On the Asymptotic Character of the Solution of the Certain Linear Differential Equations (1908).
  • [2] J. D. Tamarkin, Some General Problems of The Theory of Ordinary Linear Differential Equations And Expansions of An Arbitary Function in Series of Fundamental Functions, Math. Z. 27 (1928) 1-54.
  • [3] J. W. Lee, Spectral Properties and Oscillation Theorems for Periodic Boundary-Value Problems of Sturm Liouville Type, Journal of Differential Equations 11 (1972) 592-606.
  • [4] G. V. Berghe, M. V. Daele, H. D. Meyer, A modified difference scheme for periodic and semiperiodic Sturm-Liouville problems, Applied Numerical Mathematics 18 (1995) 69-78.
  • [5] Y. Liu, Periodic Boundary Value Problems for Higher Order Impulsive Functional Differential Equations. SDÜ Fen Edebiyat Fakültesi Fen Dergisi (E-dergi) 2 (2007) 253-272.
  • [6] D. B. Wang, Periodic Boundary Value Problems for Nonlinear First-Order Impulsive Dynamic Equations on Time Scales, Advances in Difference Equations 12 (2012).
  • [7] V. Malathi, B. S. Mohamed, B. T. Bachok, Computing Eigenvalues Of Periodic Sturm-Liouville Problems Using Shooting Technique And Direct Integration Method, International Journal of Computer Mathematics, 68 (1996) 119-132.
  • [8] K. Aydemir, O. Sh. Mukhtarov, Completeness Of One Two-Interval Boundary Value Problem With Transmission Conditions, Miskolc Mathematical Notes 15 (2014) 293-303.
  • [9] K. Aydemir, O. Sh. Mukhtarov, Class of Sturm-Liouville problems with eigen-parameter dependent transmission conditions, Numerical Functional Analysis and Optimization 38(10) (2017) 1260-1275.
  • [10] M. Kandemir, O. Sh. Mukhtarov, Nonlocal Sturm-Liouville problems with integral terms in the boundary conditions, Electronic Journal of Differential Equations 11 (2017) 112.
  • [11] O. Sh. Mukhtarov, H. Olğar, K. Aydemir, Resolvent Operator and Spectrum of New Type Boundary Value Problems, Filomat 29 (2015) 1671–1680.
  • [12] O. Sh. Mukhtarov, H. Olğar, K. Aydemir, I. Jabbarov, Operator-Pencil Realization Of One Sturm- Liouville Problem With Transmission Conditions, Applied And Computational Mathematics 17(2)(2018) 284-294.
  • [13] E. C. Titchmars, Eigenfunctions Expansion Associated with Second Order Differential Equations I, second edn. Oxford Univ. press, London 1962.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Serdar Paş 0000-0003-3722-7834

Kadriye Aydemir 0000-0002-8378-3949

Fahreddin Muhtarov 0000-0002-5482-2478

Project Number FMB-BAP 19-0391.
Publication Date December 31, 2020
Submission Date November 9, 2020
Published in Issue Year 2020 Issue: 33

Cite

APA Paş, S., Aydemir, K., & Muhtarov, F. (2020). Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems. Journal of New Theory(33), 40-49.
AMA Paş S, Aydemir K, Muhtarov F. Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems. JNT. December 2020;(33):40-49.
Chicago Paş, Serdar, Kadriye Aydemir, and Fahreddin Muhtarov. “Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems”. Journal of New Theory, no. 33 (December 2020): 40-49.
EndNote Paş S, Aydemir K, Muhtarov F (December 1, 2020) Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems. Journal of New Theory 33 40–49.
IEEE S. Paş, K. Aydemir, and F. Muhtarov, “Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems”, JNT, no. 33, pp. 40–49, December 2020.
ISNAD Paş, Serdar et al. “Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems”. Journal of New Theory 33 (December 2020), 40-49.
JAMA Paş S, Aydemir K, Muhtarov F. Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems. JNT. 2020;:40–49.
MLA Paş, Serdar et al. “Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems”. Journal of New Theory, no. 33, 2020, pp. 40-49.
Vancouver Paş S, Aydemir K, Muhtarov F. Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems. JNT. 2020(33):40-9.
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