Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results

Yi-Chou Chen

Journal of Applied Mathematics, 2015, vol. 2015, 1-6

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 .

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:516159

DOI: 10.1155/2015/516159

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