This paper is concerned with nonlocal diffusion systems of three species with delays. By modified version of Ikehara’s theorem, we prove that the traveling wave fronts of such system decay exponentially at negative infinity, and one component of such solutions also decays exponentially at positive infinity. In order to obtain more information of the asymptotic behavior of such solutions at positive infinity, for the special kernels, we discuss the asymptotic behavior of such solutions of such system without delays, via the stable manifold theorem. In addition, by using the sliding method, the strict monotonicity and uniqueness of traveling wave fronts are also obtained.
Recently, Jankowski (Appl. Math. Comput. 218:2549-2557, 2011 Appl. Math. Comput. 219:9348-9355, 2013) established four existence results for four difference equations with causal operators. These results are based on four comparison results, respectively. However, the comparison results in the above papers contain inaccuracies. In this paper, we will establish four new comparison results which correct and supplement the comparison results in the above papers. Two examples are given to illustrate our results.
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