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

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ЖУРНАЛЫ ПЕРСОНАЛИИ ОРГАНИЗАЦИИ КОНФЕРЕНЦИИ СЕМИНАРЫ ВИДЕОТЕКА ПАКЕТ AMSBIB

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Eurasian Mathematical Journal, 2013, том 4, номер 3, страницы 53–62 (Mi emj132)

Эта публикация цитируется в 11 научных статьях (всего в 11 статьях)

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

PDF полного текста (401 kB) Список цитирования (11)

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Аннотация: 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)

$L_2(0,1)$ . 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.

Ключевые слова и фразы: eigenvalues, eigenfunctions, boundary value problem, Riesz basis, ordinary differential operator, characteristic determinant.

Поступила в редакцию: 13.10.2010
Исправленный вариант: 14.02.2013

Тип публикации: Статья

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

Язык публикации: английский

Образец цитирования: 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

Цитирование в формате AMSBIB

\RBibitem{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}

Образцы ссылок на эту страницу:

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

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

Эта публикация цитируется в следующих 11 статьяx:

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”, Журн. СФУ. Сер. Матем. и физ., 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
М. А. Садыбеков, Н. С. Иманбаев, “Регулярный дифференциальный оператор с возмущенным краевым условием”, Матем. заметки, 101:5 (2017), 768–778 ; 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

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