N. S. Imanbaev, M. A. Sadybekov, “On spectral properties of a periodic problem with an integral perturbation of the boundary condition”, Eurasian Math. J., 4:3 (2013), 53

Eurasian Mathematical Journal

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Eurasian Math. J.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Eurasian Mathematical Journal, 2013, Volume 4, Number 3, Pages 53–62 (Mi emj132)

This article is cited in 11 scientific papers (total in 11 papers)

On spectral properties of a periodic problem with an integral perturbation of the boundary condition

N. S. Imanbaev^a, M. A. Sadybekov^b

^a International Kazakh-Turkish University named after A. Yasawi, Sattarhanov street, 161200 Turkestan, Kazahstan
^b Institute of Mathematics and Mathematical Modeling, Pushkin street, 125, 050010 Almaty, Kazakhstan

Full-text PDF (401 kB) Citations (11)

References:

PDF

HTML

Abstract: In this paper we consider the spectral problem for the Schrödinger equation with an integral perturbation in the periodic boundary conditions. The unperturbed problem is assumed to have the system of eigenfunctions and associated functions forming a Riesz basis in

$L_2(0,1)$ . We construct the characteristic determinant of the spectral problem. We show that the basis property of the system of root functions of the problem may fail to be satisfied under an arbitrarily small change in the kernel of the integral perturbation.

Keywords and phrases: eigenvalues, eigenfunctions, boundary value problem, Riesz basis, ordinary differential operator, characteristic determinant.

Received: 13.10.2010
Revised: 14.02.2013

Document Type: Article

MSC: 35J05, 35J08, 35J25, 35P05

Language: English

Citation: N. S. Imanbaev, M. A. Sadybekov, “On spectral properties of a periodic problem with an integral perturbation of the boundary condition”, Eurasian Math. J., 4:3 (2013), 53–62

Citation in format AMSBIB

\Bibitem{ImaSad13}

\by N.~S.~Imanbaev, M.~A.~Sadybekov

\paper On spectral properties of a~periodic problem with an integral perturbation of the boundary condition

\jour Eurasian Math. J.

\yr 2013

\vol 4

\issue 3

\pages 53--62

\mathnet{http://mi.mathnet.ru/emj132}

Linking options:

https://www.mathnet.ru/eng/emj132

https://www.mathnet.ru/eng/emj/v4/i3/p53

This publication is cited in the following 11 articles:

Nurakhmetov D., Jumabayev S., Aniyarov A., “Control of Vibrations of a Beam With Nonlocal Boundary Conditions”, Int. J. Math. Phys.-Kazakhstan, 12:2 (2021), 45–49
Polyakov D.M., “Nonlocal Perturbation of a Periodic Problem For a Second-Order Differential Operator”, Differ. Equ., 57:1 (2021), 11–18
Nurlan S. Imanbaev, “On a problem that does not have basis property of root vectors, associated with a perturbed regular operator of multiple differentiation”, Zhurn. SFU. Ser. Matem. i fiz., 13:5 (2020), 568–573
O. Sh. Mukhtarov, K. Aydemir, “Minimization principle and generalized Fourier series for discontinuous Sturm-Liouville systems in direct sum spaces”, J. Appl. Anal. Comput., 8:5 (2018), 1511–1523
K. Aydemir, H. Olgar, O. Sh. Mukhtarov, F. Muhtarov, “Differential operator equations with interface conditions in modified direct sum spaces”, Filomat, 32:3 (2018), 921–931
M. A. Sadybekov, N. S. Imanbaev, “A Regular Differential Operator with Perturbed Boundary Condition”, Math. Notes, 101:5 (2017), 878–887
N. S. Imanbaev, M. A. Sadybekov, “About characteristic determinant of one boundary value problem not having the basis property”, International Conference Functional Analysis in Interdisciplinary Applications FAIA 2017, AIP Conf. Proc., 1880, eds. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 050002
M. A. Sadybekov, N. S. Imanbaev, “Characteristic determinant of a boundary value problem, which does not have the basis property”, Eurasian Math. J., 8:2 (2017), 40–46
N. S. Imanbaev, “Characteristic determinant of the spectral problem for the Sturm-Liouville operator with the perturbed boundary value conditions”, Bull. Karaganda Univ-Math., 82:2 (2016), 68–73
N. Imanbaev, “Stability of the basis property of system of root functions of Sturm-Liouville operator with integral boundary condition”, Applications of Mathematics in Engineering and Economics, AMEE'16, AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040026
Imanbaev N.S., “On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator With An Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems”, Int. J. Differ. Equat., 2015, 641481

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	528
Full-text PDF :	194
References:	79

Что такое QR-код?

Registration to the website

Logotypes