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On the Spectrum of a Nonlinear Two Parameter Matrix Eigenvalue Problem

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Book cover Applications of Nonlinear Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 134))

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.

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Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva, Israel

    Michael Gil’

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  1. Michael Gil’
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Correspondence to Michael Gil’ .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Gil’, M. (2018). On the Spectrum of a Nonlinear Two Parameter Matrix Eigenvalue Problem. In: Rassias, T. (eds) Applications of Nonlinear Analysis . Springer Optimization and Its Applications, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-89815-5_13

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