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 Eurasian Math. J., 2013, Volume 4, Number 3, Pages 20–31 (Mi emj130)

An inverse problem for the matrix quadratic pencil on a finite interval

N. P. Bondarenko

Department of Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, 410026, Russia

Abstract: We consider a quadratic matrix boundary value problem with equations and boundary conditions dependent on a spectral parameter. We study an inverse problem that consists in recovering the differential pencil by the so-called Weyl matrix. We obtain asymptotic formulas for the solutions of the considered matrix equation. Using the ideas of the method of spectral mappings, we prove the uniqueness theorem for this inverse problem.

Keywords and phrases: matrix quadratic differential pencils, Weyl matrix, inverse spectral problems, method of spectral mappings.

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MSC: 34A55, 34B07, 34B24, 34L40, 47E05
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Citation: N. P. Bondarenko, “An inverse problem for the matrix quadratic pencil on a finite interval”, Eurasian Math. J., 4:3 (2013), 20–31

Citation in format AMSBIB
\Bibitem{Bon13} \by N.~P.~Bondarenko \paper An inverse problem for the matrix quadratic pencil on a finite interval \jour Eurasian Math. J. \yr 2013 \vol 4 \issue 3 \pages 20--31 \mathnet{http://mi.mathnet.ru/emj130} 

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• http://mi.mathnet.ru/eng/emj/v4/i3/p20

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This publication is cited in the following articles:
1. N. Bondarenko, “Recovery of the matrix quadratic differential pencil from the spectral data”, J. Inverse Ill-Posed Probl., 24:3 (2016), 245–263
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