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

Yıl 2019, Cilt: 8 Sayı: 2, 37 - 41, 31.12.2019

Osman Yılmaz , Mustafa Kandemir , Kadriye Aydemir

Öz

In this study, we examine some spectral properties of a new type periodic eigenvalue problem for the
dierential 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

Anahtar Kelimeler

Periodic Sturm-Liouville Problem

Destekleyen Kurum

Amasya University

Proje Numarası

FMB-BAP 19-0391.

Kaynakça

• [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.