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Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results

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  • Yi-Chou Chen

Abstract

Let be a real-valued polynomial function in which the degree of in is greater than or equal to 1. For any polynomial , we assume that is a nonlinear operator with . In this paper, we will find an eigenfunction to satisfy the following equation: for some eigenvalue and we call the problem a fixed point like problem. If the number of all eigenfunctions in is infinitely many, we prove that (i) any coefficients of , are all constants in and (ii) is an eigenfunction in if and only if .

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  • Yi-Chou Chen, 2015. "Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-6, February.
    • Handle: RePEc:hin:jnljam:516159
    DOI: 10.1155/2015/516159
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