SOME REMARKS ON LATTICE AND NONLOCAL DISPERSAL EVOLUTION SYSTEMS

In this paper, we first characterize the continuity of a map in the space C = BC(H, R-m) equipped with the compact open topology. Then we show that linear lattice and nonlocal dispersal equations generate uniformly continuous semigroups in the Banach space B = BC(H, R-m) 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.