On the Spectrum of a Nonlinear Two Parameter Matrix Eigenvalue Problem

Michael Gil’ ()
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Michael Gil’: Ben Gurion University of the Negev

A chapter in Applications of Nonlinear Analysis, 2018, pp 387-402 from Springer

Abstract: Abstract We consider the nonlinear two parameter eigenvalue problem (T p − λ 1 A p1 − λ 2 A p2 − λ 1 λ 2 A p3)v p = 0, where λ 1, λ 2 ∈C; T p, A pk (p = 1, 2;k = 1, 2, 3) are matrices. Bounds for the spectral radius of that problem are suggested. Our main tool is the recent norm estimates for the resolvent of an operator on the tensor product of Euclidean spaces. In addition, we investigate perturbations of the considered problem and derive a Gershgorin type bounds for the spectrum. It is shown that the main result of the paper is sharp.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-89815-5_13

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DOI: 10.1007/978-3-319-89815-5_13

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