TRAVELING WAVEFRONTS FOR A DISCRETE DIFFUSIVE LOTKA-VOLTERRA COMPETITION SYSTEM WITH NONLOCAL NONLINEARITIES

This article concerns the traveling wavefronts of a discrete diffusive Lotka-Volterra competition system with nonlo cal nonlinearities. We first prove that there exists a c(& lowast;) > 0 such that when the wave speed is large than or equals to c(& lowast;), the system admits an increasing traveling wavefront connecting two boundary equilibria by the upper-lower solutions method. Furthermore, we prove that (i) all traveling wavefronts with speed c > c(& lowast;)(> c(& lowast;)) are globally stable with exponential convergence rate t(-1/2e-epsilon tau sigma t), where sigma > 0 and epsilon(tau) = epsilon(tau) is an element of (0, 1) is a decreasing function for the time delay tau > 0; (ii) the traveling wavefronts with speed c = c(& lowast;) are globally algebraically stable in the algebraic form t(-1/2). The approaches are the weighted energy method, the comparison principle and Fourier transform.