Some remarks on lattice and nonlocal dispersal evolution systems

Abstract

<p style='text-indent:20px;'>In this paper, we first characterize the continuity of a map in the space <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{C} = BC(\mathcal{H},\mathbb{R}^m) $\end{document}</tex-math></inline-formula> equipped with the compact open topology. Then we show that linear lattice and nonlocal dispersal equations generate uniformly continuous semigroups in the Banach space <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{B} = BC(\mathcal{H},\mathbb{R}^m) $\end{document}</tex-math></inline-formula> equipped with the supremum norm. Finally, we illustrate how to prove nonlinear lattice and nonlocal dispersal equations generate monotone semiflows with respect to the compact open topology.</p>