[Nonlinear eigenproblems] The following will be elaborated shortly after I put in today's calculations into the computing cluster:
Let $f,g,h \in \mathcal{F}(\Bbb{F})$, $h$ fixed,$x \in \Bbb{F}^n$, $\lambda \in \Bbb{F},A \in M_n(\Bbb{F}) \text{ or }L^p(\Bbb{F})$
General nonlinear eigenvalue problem:
$f(g)=\lambda g$
Matrix function eigenvalue problem
$A(\lambda)x = 0$
Polynomial eigenvalue problem:
$\left(\sum_{k=1}^nA_k\lambda^k\right)x=0$
"Constant image" maps and eigenproblem:
Given $\forall g, f(g)=h$