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On the Spectral Properties of a Fourth-Order Self-Adjoint Operator
- Authors: Polyakov D.M1
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Affiliations:
- Southern Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362025, Russia
- Issue: Vol 59, No 2 (2023)
- Pages: 164-169
- Section: Articles
- URL: https://rjmseer.com/0374-0641/article/view/649407
- DOI: https://doi.org/10.31857/S0374064123020036
- EDN: https://elibrary.ru/PTUFRY
- ID: 649407
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Abstract
We consider a spectral problem for a fourth-order differential operator with real periodic coefficients and Neumann-type boundary conditions. For this operator, the eigenvalue asymptotics and a regularized trace formula are obtained.
About the authors
D. M Polyakov
Southern Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362025, Russia
Author for correspondence.
Email: DmitryPolyakow@mail.ru
г. Владикавказ, Россия
References
- Gupta C.P. Existence and uniqueness theorems for some fourth order fully quasilinear boundary value problems // Appl. Anal. 1990. V. 36. P. 157-169.
- Peletier L.A., Rodrigues J.A. Homoclinic orbits to a saddle-center in a fourth-order differential equation // J. Differ. Equat. 2004. V. 203. P. 185-215.
- McLaughlin J.R. An inverse eigenvalue problem of order four - an infinite case // SIAM J. Math. Anal. 1978. V. 9. № 3. P. 395-413.
- Caudill Jr L.F., Perry P.A., Schueller A.W. Isospectral sets for fourth-order ordinary differential operators // SIAM J. Math. Anal. 1998. V. 29. № 4. P. 935-966.
- Boumenir A. Sampling for the fourth-order Sturm-Liouville differential operator // J. Math. Anal. Appl. 2003. V. 278. P. 542-550.
- Керимов Н.Б., Алиев З.С. О базисности системы собственных функций одной спектральной задачи со спектральным параметром в граничном условии // Дифференц. уравнения. 2007. Т. 43. № 7. С. 886-895.
- Поляков Д.М. Спектральный анализ несамосопряжённого оператора четвёртого порядка с негладкими коэффициентами // Сиб. мат. журн. 2015. Т. 56. № 1. С. 165-184.
- Ma R., Wang H., Elsanosi M. Spectrum of a linear fourth-order differential operator and its applications // Math. Nachr. 2013. V. 286. P. 1805-1819.
- Наймарк М.А. Линейные дифференциальные операторы. М., 1969.
- Баданин А.В., Коротяев Е.Л. Спектральные оценки для периодического оператора четвёртого порядка // Алгебра и анализ. 2010. Т. 22. № 5. С. 1-48.
- Badanin A., Korotyaev E.L. Third-order operators with three-point conditions associated with Boussinesq's equation // Appl. Anal. 2021. V. 100. P. 527-560.
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