Abstract
A stabilization theorem for discrete strongly monotone and nonexpansive dynamical systems on a Banach lattice is proved. This result is applied to a periodic-parabolic semilinear initial-boundary value problem to show the convergence of solutions towards periodic solutions.
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Alikakos, N.D., Hess, P. On stabilization of discrete monotone dynamical systems. Israel J. Math. 59, 185–194 (1987). https://doi.org/10.1007/BF02787260
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DOI: https://doi.org/10.1007/BF02787260