  This chapter describes how gradient flows and nonlinear power methods in
Banach spaces can be used to solve nonlinear eigenvector-dependent eigenvalue
problems, and how convergence of (discretized) approximations can be verified.
We review several flows from literature, which were proposed to compute
nonlinear eigenfunctions, and show that they all relate to normalized gradient
flows. Furthermore, we show that the implicit Euler discretization of gradient
flows gives rise to a nonlinear power method of the proximal operator and prove
their convergence to nonlinear eigenfunctions. Finally, we prove that
$\Gamma$-convergence of functionals implies convergence of their ground states,
which is important for discrete approximations.
