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Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities

Year 2019, Volume: 8 Issue: 2, 37 - 41, 31.12.2019

Osman Yılmaz Mustafa Kandemir Kadriye Aydemir

Abstract

In this study, we examine some spectral properties of a new type periodic eigenvalue problem for the
di erential equation
􀀀 y00 + q(x)y = y; x 2 [a; c) [ (c; b] (0.1)
together with the periodic boundary conditions at the end-points x = a; b given by
y(a) = y(b); y0(a) = y0(b) (0.2)
and with the interface conditions at the interior point of singularity x = c; given by
y(c+) = y(c􀀀); y0(c+) = y0(c􀀀) (0.3)
where q(x) is the continuous function, , are real numbers and  is complex eigenvalue parameter

Keywords

Periodic Sturm-Liouville Problem

Supporting Institution

Amasya University

Project Number

FMB-BAP 19-0391.

References

  • [1] P. B. Allahverdiev, E. Bairamov, E. Ugurlu, Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions,J. Math. Anal. Appl., 401(2013), 388-396.
  • [2] M. Kandemir, O. Sh. Mukhtarov, Solvability of fourth order Sturm -Liouville problems with abstract linear functionals in boundarytransmission conditions, DOI: 10.1002/mma.4852,´aMath Meth Appl Sci. (2018) 1ˆu10.
  • [3] O. Sh. Mukhtarov and K. Aydemir, Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, ´aActa Mathematica Scientia (2015) 35B(3):639ˆu649.
  • [4] E. S. Panakhov and M. Sat, Reconstruction of potential function for Sturm-Liouville operator with coulomb potential Boundary Value Problems, 49(2013), pp.2013.
  • [5] W.A. Woldegerima, The Sturm-Liouville Boundary Value Problems and their applications: First Edition, LAP Lambert Academic Publishing. (2011).
  • [6] L. Schovanec, D. Gilliam , Chapter 5. Sturm-Liouville Theory Mathematics and Statistics Texas Tech University (1998-1999).
  • [7] M. Y¨ucel, O. Sh. Mukhtarov, A New Treatment of the Decomposition Method for Nonclassical Boundary Value Problems, Journal of Advanced Physics, 2018, 7(2), 161–166.

Year 2019, Volume: 8 Issue: 2, 37 - 41, 31.12.2019

Osman Yılmaz Mustafa Kandemir Kadriye Aydemir

Abstract

Project Number

FMB-BAP 19-0391.

References

  • [1] P. B. Allahverdiev, E. Bairamov, E. Ugurlu, Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions,J. Math. Anal. Appl., 401(2013), 388-396.
  • [2] M. Kandemir, O. Sh. Mukhtarov, Solvability of fourth order Sturm -Liouville problems with abstract linear functionals in boundarytransmission conditions, DOI: 10.1002/mma.4852,´aMath Meth Appl Sci. (2018) 1ˆu10.
  • [3] O. Sh. Mukhtarov and K. Aydemir, Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, ´aActa Mathematica Scientia (2015) 35B(3):639ˆu649.
  • [4] E. S. Panakhov and M. Sat, Reconstruction of potential function for Sturm-Liouville operator with coulomb potential Boundary Value Problems, 49(2013), pp.2013.
  • [5] W.A. Woldegerima, The Sturm-Liouville Boundary Value Problems and their applications: First Edition, LAP Lambert Academic Publishing. (2011).
  • [6] L. Schovanec, D. Gilliam , Chapter 5. Sturm-Liouville Theory Mathematics and Statistics Texas Tech University (1998-1999).
  • [7] M. Y¨ucel, O. Sh. Mukhtarov, A New Treatment of the Decomposition Method for Nonclassical Boundary Value Problems, Journal of Advanced Physics, 2018, 7(2), 161–166.
There are 7 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Osman Yılmaz

Mustafa Kandemir

Kadriye Aydemir

Project Number FMB-BAP 19-0391.
Publication Date December 31, 2019
Published in Issue Year 2019 Volume: 8 Issue: 2

Cite

APA Yılmaz, O., Kandemir, M., & Aydemir, K. (2019). Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities. Journal of New Results in Science, 8(2), 37-41.
AMA Yılmaz O, Kandemir M, Aydemir K. Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities. JNRS. December 2019;8(2):37-41.
Chicago Yılmaz, Osman, Mustafa Kandemir, and Kadriye Aydemir. “Eigenvalues and Eigenfunctions of the Periodic Sturm-Liouville Problems With Discontinuities”. Journal of New Results in Science 8, no. 2 (December 2019): 37-41.
EndNote Yılmaz O, Kandemir M, Aydemir K (December 1, 2019) Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities. Journal of New Results in Science 8 2 37–41.
IEEE O. Yılmaz, M. Kandemir, and K. Aydemir, “Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities”, JNRS, vol. 8, no. 2, pp. 37–41, 2019.
ISNAD Yılmaz, Osman et al. “Eigenvalues and Eigenfunctions of the Periodic Sturm-Liouville Problems With Discontinuities”. Journal of New Results in Science 8/2 (December 2019), 37-41.
JAMA Yılmaz O, Kandemir M, Aydemir K. Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities. JNRS. 2019;8:37–41.
MLA Yılmaz, Osman et al. “Eigenvalues and Eigenfunctions of the Periodic Sturm-Liouville Problems With Discontinuities”. Journal of New Results in Science, vol. 8, no. 2, 2019, pp. 37-41.
Vancouver Yılmaz O, Kandemir M, Aydemir K. Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities. JNRS. 2019;8(2):37-41.


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