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 .
"Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results." J. Appl. Math. 2015 (SI5) 1 - 6, 2015. https://doi.org/10.1155/2015/516159