The Spectral Properties of a Two-Term Fourth-Order Operator with a Spectral Parameter in the Boundary Condition

We consider a spectral problem for a two-term fourth-order differential operator with nonsmooth potential. The boundary conditions involve a spectral parameter. We obtain eigenvalue asymptotics at high energy and a regularized trace formula for this operator.

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Bibliographic Details
Published in:	Siberian mathematical journal Vol. 64; no. 3; pp. 649 - 669
Main Author:	Polyakov, D. M.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-05-2023 Springer Nature B.V
Subjects:	Boundary conditions Differential equations Eigenvalues Mathematics Mathematics and Statistics Operators (mathematics) Parameters spectral parameter in boundary conditions eigenvalue asymptotics fourth-order differential operator trace formula 517.927
Online Access:	Get full text
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Description
Summary:	We consider a spectral problem for a two-term fourth-order differential operator with nonsmooth potential. The boundary conditions involve a spectral parameter. We obtain eigenvalue asymptotics at high energy and a regularized trace formula for this operator.
ISSN:	0037-4466 1573-9260
DOI:	10.1134/S0037446623030138