Existence of forced waves for a 2-D lattice differential equation in a time-periodic shifting habitat

Abstract

This paper is concerned about the existence of forced waves for a 2-D lattice differential equation in a time-periodic shifting habitat. First, we study the corresponding initial value problem and establish the comparison principle. Then we investigate the asymptotic spreading speed $ c_{*} $ and periodic traveling waves for a 2-D lattice differential equation without shifting habitat. Finally, by constructing a pair of upper and lower solutions and using the monotone iteration technique, we establish the existence of periodic forced waves with the speed at which the habitat is shifting.