Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument

Erdoğan Şen

doi:10.17776/csj.416602

EN TR

Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument

Abstract

In this study, a formula for regularized sums of eigenvalues and nodal points of eigenfunctions for a discontinuous Sturm-Liouville problem with a constant retarded argument. Contrary to standart problems the spectral parameter appears not only in the differential equation, but also in one of the boundary conditions. Thus, we see whether the nodal points of eigenfunctions and the trace change or not.

Keywords

Differential equation with retarded argument,transmission conditions,spectrum,nodal points,regularized trace

References

[1]. Norkin S.B., Differential equations of the second order with retarded argument, Translations of Mathematical Monographs, AMS, Providence, RI, 1972.
[2]. Mukhtarov O.Sh., Kadakal M., Muhtarov F.S., On discontinuous Sturm-Liouville problems with transmission conditions, J. Math. Kyoto Univ., 44-4 (2004) 779-798.
[3]. Mukhtarov O.Sh., Tunç E., Eigenvalue problems for Sturm--Liouville equations with transmission conditions, Israel J. Math. 144 (2004) 367--380.
[4]. Aydemir K., Mukhtarov O.Sh., Class of Sturm-Liouville problems with eigenparameter dependent transmission conditions, Numer. Funct. Anal. Optim., 38-10 (2017) 1260-1275.
[5]. Çakmak Y., Keskin B., Uniqueness theorems for Sturm-Liouville operator with parameter dependent boundary conditions and finite number of transmission conditions, Cumhuriyet Sci. J., 38-3 (2017) 535-543.
[6]. Kandemir M., Asymptotic distribution of eigenvalues for fourth-order boundary-value problem with discontinuous coefficients and transmission conditions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 66-1 (2017) 133-152.
[7]. Li K., Sun J., Hao X., Weyl function of Sturm-Liouville problems with transmission conditions at finite interior points, Mediter. J. Math., 14-189 (2017) 1-15.
[8]. Uğurlu E., Taş K., A new method for dissipative dynamic operator with transmission conditions, Complex Anal. Oper. Theory, 12 (2018) 1027-1055.

[9]. Zettl A., Adjoint and self-adjoint boundary value problems with interface conditions, SIAM J. Appl. Math., 16 (1968) 851-859.
[10]. Buschmann D., Stolz G., Weidmann J., One-dimensional Schrödinger operators with local point interactions, J. Reine Angew. Math., 467 (1995) 169-186.
[11]. Gelfand I.M., Levitan B.M., On a formula for eigenvalues of a differential operator of second order, Doklady Akademii Nauk SSSR, 88 (1953) 593--596 (Russian).
[12]. Dikii L.A., Trace formulas for Sturm-Liouville differential equations, Uspekhi Mat. Nauk, 12-3 (1958) 111-143.
[13]. Maksudov F.G., Bayramoglu M., Adıguzelov E., On a regularized traces of the Sturm-Liouville operator on a finite interval with the unbounded operator coefficient, Doklady Akademii Nauk SSSR, 277-4 (1984); English translation: Soviet Math. Dokl., 30 (1984) 169-173.
[14]. Bayramoglu M., Sahinturk H., Higher order regularized trace formula for the regular Sturm-Liouville equation contained spectral parameter in the boundary condition, Appl. Math. Comput., 186 (2007) 1591-1599.
[15]. Gül E., On the regularized trace of a second order differential operator, Appl. Math. Comput., 198 (2008) 471-480.
[16]. Yang C-F., Trace and inverse problem of a discontinuous Sturm-Liouville operator with retarded argument, J. Math. Anal. Appl., 395 (2012) 30-41.
[17]. Bayramoglu M., Bayramov A., Şen E., A regularized trace formula for a discontinuous Sturm-Liouville operator with delayed argument, Electronic Journal of Differential Equations, 2017-104 (2017) 1-12.
[18]. Hira F., A trace formula for the Sturm-Liouville type equation with retarded argument, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 66-1 (2017) 124-132.
[19]. Keskin B., Ozkan A.S., Inverse nodal problems for impulsive Sturm-Liouville equation with boundary conditions depending on the parameter, Advances in Analysis, 2-3 (2017) 151-156.
[20]. Keskin B., Reconstruction of the Volterra-type integro-differential operator from nodal points, Boundary Value Problems, 2018-47 (2018) 1-8.
[21]. Keskin B., Ozkan A.S., Inverse nodal problems for Dirac-type integro-differential operators, J. Differ. Eq., 263 (2017) 8838-8847.
[22]. Bayramov A., Çalışkan S., Uslu S., Computation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument, Appl. Math. Comput., 191 (2007) 592-600.
[23]. Şen E., Bayramov A., Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the boundary condition, Math. Comput. Model., 54-(11-12) (2011) 3090-3097.
[24]. Yurko V.A., Inverse Spectral Problems for Differential Operators and Their Applications, Gordon and Breach, Amsterdam, 2000.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Erdoğan Şen
0000-0001-6603-2652
Türkiye

Publication Date

September 30, 2018

Submission Date

April 18, 2018

Acceptance Date

September 28, 2018

Published in Issue

Year 2018 Volume: 39 Number: 3

DOI

https://doi.org/10.17776/csj.416602

IZ

https://izlik.org/JA34NW64AG

Cite

RIS / Bibtex

APA

Şen, E. (2018). Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument. Cumhuriyet Science Journal, 39(3), 597-607. https://doi.org/10.17776/csj.416602

AMA

1.Şen E. Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument. CSJ. 2018;39(3):597-607. doi:10.17776/csj.416602

Chicago

Şen, Erdoğan. 2018. “Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem With Retarded Argument”. Cumhuriyet Science Journal 39 (3): 597-607. https://doi.org/10.17776/csj.416602.

EndNote

Şen E (September 1, 2018) Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument. Cumhuriyet Science Journal 39 3 597–607.

IEEE

[1]E. Şen, “Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument”, CSJ, vol. 39, no. 3, pp. 597–607, Sept. 2018, doi: 10.17776/csj.416602.

ISNAD

Şen, Erdoğan. “Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem With Retarded Argument”. Cumhuriyet Science Journal 39/3 (September 1, 2018): 597-607. https://doi.org/10.17776/csj.416602.

JAMA

1.Şen E. Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument. CSJ. 2018;39:597–607.

MLA

Şen, Erdoğan. “Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem With Retarded Argument”. Cumhuriyet Science Journal, vol. 39, no. 3, Sept. 2018, pp. 597-0, doi:10.17776/csj.416602.

Vancouver

1.Erdoğan Şen. Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument. CSJ. 2018 Sep. 1;39(3):597-60. doi:10.17776/csj.416602

Cited By

Sınır Koşulunda Öz Parametre Bulunduran Bir Sturm-Liouville Operatörü İçin Ters Nodal Problem

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi

https://doi.org/10.17714/gumusfenbil.672966

Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument

Abstract

Keywords

Geciken Argümanlı Bir Sturm-Liouville Probleminin İzinin ve Özfonksiyonlarının Düğüm Noktalarının Hesaplanması

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

Cited By

Sınır Koşulunda Öz Parametre Bulunduran Bir Sturm-Liouville Operatörü İçin Ters Nodal Problem