Abstract
In this paper, we consider the asymptotic behavior and uniqueness of traveling wave fronts connecting two half-positive equilibria in a competitive recursion system. We first prove that these traveling wave fronts have the exponential decay rates at the minus/plus infinity, where for a given wave speed, there are three possible asymptotic behaviors for the first component of the wave profile at the plus infinity and the second component of the wave profile at the minus infinity, respectively. And then we use the sliding method to prove the uniqueness of traveling wave fronts for this system. Furthermore, by combining uniqueness and upper and lower solutions technique, we also give the exact decay rate of the weaker competitor under certain conditions.
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Acknowledgments
We would like to thank two referees for their careful reading and helpful suggestions which led to an improvement of our original manuscript. Kun Li was supported by the National Natural Science Foundation of China (Grant No. 11401198), the Hunan Provincial Natural Science Foundation of China (Grant No. 2015JJ3054), the Project Funded by China Postdoctoral Science Foundation (Grant No. 2015M582882), the Provincial Natural Science Foundation of the Higher Educational Institutions of Anhui Province of China (Grant No. KJ2013B245), and the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province. Jianhua Huang was supported by the National Natural Science Foundation of China (Grant No. 11371367). Xiong Li was supported by the National Natural Science Foundation of China (Grant No. 11571041) and the Fundamental Research Funds for the Central Universities.
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Li, K., Huang, J., Li, X. et al. Asymptotic behavior and uniqueness of traveling wave fronts in a competitive recursion system. Z. Angew. Math. Phys. 67, 144 (2016). https://doi.org/10.1007/s00033-016-0739-7
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DOI: https://doi.org/10.1007/s00033-016-0739-7