Southern Mathematical Institute
Vladikavkaz Scientific Center of RAS
362025, 53 Vatutin str., Vladikavkaz, Russia
email: DmitryPolyakow@mail.ru
Dmitry M. Polyakov
Abstract:
We consider a spectral problem for a fourth-order differential equation with
spectral parameter dependent boundary conditions. We determine the high
energy eigenvalue behavior for this operator. Moreover, if the coefficient of
differential equation is sufficiently smooth, we can obtain sharp eigenvalue
asymptotic behavior. This behavior exhibits a non-standard high-frequency
effect generated by the spectral parameter in the boundary conditions.
Submitted July 23, 2024. Published October 16, 2024.
Math Subject Classifications: 34L20, 34B08, 34B09.
Key Words: Eigenvalue; asymptotic behavior; fourth-order eigenvalue problem;
spectral parameter in boundary conditions; fourth-order differential operator.
DOI: 10.58997/ejde.2024.62
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Dmitry M. Polyakov Southern Mathematical Institute Vladikavkaz Scientific Center of RAS 362025, 53 Vatutin str., Vladikavkaz, Russia email: DmitryPolyakow@mail.ru |
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