Abstract
This paper deals with quadratic operator pencils $$ L(\lambda ) = \lambda ^2 A + \lambda B + C, $$ where A, B are non-invertible non-negative operators and C is a selfadjoint operator, which is bounded from below and has a compact resolvent. Such pencils naturally arise in stability problems of mechanics and resistive magnetohydrodynamics. Under certain assumptions on A, B and C the description of the spectrum of the pencil L is given.KeywordsQuadratic operator pencilsSpectrumessential spectrumnormal eigenvalue
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