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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 |
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| Abstract: |
| 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. |
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