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Traveling Wave Solutions in an Integrodifference Equation with Weak Compactness
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KeyWord:Generalized upper and lower solutions; Traveling wave map; Minimal wave speed; Decay behavior
Author NameAffiliation
Shuxia Pan School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050,China 
Guo Lin School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China 
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      This article studies the existence of traveling wave solutions in an integrodifference equation with weak compactness. Because of the special kernel function that may depend on the Dirac function, traveling wave maps have lower regularity such that it is difficult to directly look for a traveling wave solution in the uniformly continuous and bounded functional space. In this paper, by introducing a proper set of potential wave profiles, we can obtain the existence and precise asymptotic behavior of nontrivial traveling wave solutions, during which we do not require the monotonicity of this model.