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Please use this identifier to cite or link to this item: https://oldena.lpnu.ua/handle/ntb/42792
Title: Boundary-value problem for second-order differential-operator equation with involution
Other Titles: Крайова задача для диференціально-операторного рівняння другого порядку з інволюцією
Authors: Баранецький, Я. О.
Коляса, Л. І.
Baranetskij, Ya. O.
Kolyasa, L. I.
Affiliation: Нацiональний унiверситет “Львiвська полiтехнiка”
Lviv Polytechnic National University
Bibliographic description (Ukraine): Baranetskij Ya. O. Boundary-value problem for second-order differential-operator equation with involution / Ya. O. Baranetskij, L. I. Kolyasa // Вісник Національного університету «Львівська політехніка». Серія: Фізико-математичні науки. — Львів : Видавництво Львівської політехніки, 2017. — № 871. — С. 20–26.
Bibliographic description (International): Baranetskij Ya. O. Boundary-value problem for second-order differential-operator equation with involution / Ya. O. Baranetskij, L. I. Kolyasa // Visnyk Natsionalnoho universytetu "Lvivska politekhnika". Serie: Fizyko-matematychni nauky. — Lviv : Vydavnytstvo Lvivskoi politekhniky, 2017. — No 871. — P. 20–26.
Is part of: Вісник Національного університету «Львівська політехніка». Серія: Фізико-математичні науки, 871, 2017
Journal/Collection: Вісник Національного університету «Львівська політехніка». Серія: Фізико-математичні науки
Issue: 871
Issue Date: 28-Mar-2017
Publisher: Видавництво Львівської політехніки
Place of the edition/event: Львів
UDC: 517.95
Keywords: диференціальне рівняння
диференціально-операторне рівняння
коренева фун- кція
оператор інволюції
несамоспряжений оператор
базис Рісса
нелокальна задача
differential equation
differential operator equation
root function
operator of involution
essentially a nonself adjoint operator
Riesz basis
nonlocal problem
Number of pages: 7
Page range: 20-26
Start page: 20
End page: 26
Abstract: Вивчається нелокальна двоточкова задача для диференцiально-операторних рiвнянь з iнволюцi- єю. Встановлено спектральнi властивостi та умови iснування i єдиностi розв’язку. Наведено доста- тнi умови, за яких система кореневих функцiй задачi утворює базис Рiсса.
We study a nonlocal problem for differential operator equations of order 2 with involution. The spectral properties of the operator of this problem are analyzed and the conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.
URI: https://ena.lpnu.ua/handle/ntb/42792
Copyright owner: Національний університет „Львівська політехніка“, 2017
© Ya. O. Baranetskij, L. I. Kolyasa, 2017
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[9] Kopzhassarova A. A., Lukashov A. L., Sarsenbi A. M. Spectral properties of non-self-adjoint perturbations for a spectral problem with involution, Abstr. Appl. Anal, 2012, P. 1–5.
[10] Wiener J., Aftabizadeh A. R. Boundary value problems for differential equations with reflection of the argument, Int. J. Math. Math. Sci, 1985, 8, N 1. –P. 151–163.
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[17] Kritskov L. V., Sarsenbi A. M. Spectral properties of a nonlocal problem for the differential equation with involution, Differ. Equ, 2015, 51, N 8, P. 984–990.
[18] Kurdyumov V. P. On Riesz bases of eigenfunction of 2-nd order differential operator with involution and integral boundary conditions, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform, 2015, 15, N 4. –P. 392–405.
[19] O’Regan D. Existence results for differential equations with reflection of the argument, J. Aust. Math. Soc. –1994, A 57, N 2, P. 237–260.
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[21] Sadybekov M. A., Sarsenbi A. M. Mixed problem for a differential equation with involution under boundary conditions of general form, First Internati- onal Conference on Analysis and Applied Mathemati- cs: ICAAM 2012. AIP Conference Proceedings. –2012, 1470, P. 225–227.
[22] Sarsenbi A. M., Tengaeva A. A. On the basis properti- es of root functions of two generalized eigenvalue problems, Differentsialnye Uravneniya, 2012, 48,N 2, P. 306–308.
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[27] Shkalikov A. A. On the basis problem of the ei- genfunctions of an ordinary differential operator, Uspekhi Mat. Nauk, 1979, 34, N 5, P. 235–236.
[28] D’yachenko A. V., Shkalikov A. A. On a Model Problem for the Orr-Sommerfeld Equation with Linear Profile, Funct. Anal. Appl, 2002, 36, N 3, P. 228–232.
[29] Tumanov S. N., Shkalikov A. A. On the Spectrum Localization of the Orr-Sommerfeld Problem for Large Reynolds Numbers, Math. Notes, 2002, 72, N 4. –P. 519–526.
[30] Shkalikov A. A. Spectral Portraits of the Orr- Sommerfeld Operator with Large Reynolds Numbers, J. Math. Sci, 2004, 124, N 6, P. 5417–5441.
[31] Ashurov R. R. Biorthogonal expansions of a nonself- adjoint Schrdinger operator, Differ. Uravn, 1991. –27, N 1, P. 156–158.
[32] Lidskii V. B. An estimate for the resolvent of an elliptic differential operator, Funct. Anal. Appl, 1976, 10,N 4, P. 324–325.
[33] Makin A. S. Spectral analysis of a boundary value problem for the Schrodinger operator with complex potential, Differ. Uravn, 1994. –y 30, N 12. –P. 1903–1912.
[34] Hokhberh I. Ts., Krein M. H. Vvedenie v teoriiu li- neinykh nesamosopriazhennykh operatorov v hilber- tovom prostranstve, M., Nauka, 1965, 448 p.
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