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On the Spectrum of a Nonlinear Two Parameter Matrix Eigenvalue Problem

In: Applications of Nonlinear Analysis

Author

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  • Michael Gil’

    (Ben Gurion University of the Negev)

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.

Suggested Citation

  • Michael Gil’, 2018. "On the Spectrum of a Nonlinear Two Parameter Matrix Eigenvalue Problem," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Applications of Nonlinear Analysis, pages 387-402, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-89815-5_13
    DOI: 10.1007/978-3-319-89815-5_13
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