This article is cited in 11 papers

Asymptotics of the Spectrum of Nonsmooth Perturbations of Differential Operators of Order $2m$

È. F. Akhmerova

Bashkir State University

Abstract: On a finite closed interval, we obtain the asymptotics of the eigenvalues of a differential operator of order $2m$ perturbed by a differential operator of order $2m-2$ given by a quasidifferential expression. We also consider the case of multiple eigenvalues.

Keywords: perturbation of a differential operator, spectrum of perturbations, quasidifferential expression, Hilbert space, Dirichlet boundary conditions, resolvent of an operator.

UDC: 517.984

Received: 27.04.2009
Revised: 25.02.2010

DOI: 10.4213/mzm8407

 English version: Mathematical Notes, 2011, 90:6, 813–823

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