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Front-like Entire Solutions for a Lotka-Volterra Weak Competition System with Nonlocal Dispersal

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Abstract

This paper is concerned with the front-like entire solutions for a Lotka-Volterra weak competition system with nonlocal dispersal. Here, an entire solution means a classical solution defined for all space and time variables. This system has traveling wavefronts and enjoys the comparison principle. Based on these traveling wavefronts, we construct some super- and sub-solutions. Then, by using the comparison principle and the super- and sub-solutions method, we establish the existence of front-like entire solutions which behave as two wavefronts coming from the both sides of x-axis. Moreover, some properties of the front-like entire solutions are obtained.

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Funding

The second author was supported by NSF of China (11861056) and NSF of Gansu Province (18JR3RA093).

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Authors and Affiliations

  1. Colloge of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, Gansu, People’s Republic of China

    Qian Zhang & Guo-Bao Zhang

Authors
  1. Qian Zhang
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  2. Guo-Bao Zhang
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Correspondence to Guo-Bao Zhang.

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Zhang, Q., Zhang, GB. Front-like Entire Solutions for a Lotka-Volterra Weak Competition System with Nonlocal Dispersal. J Dyn Control Syst 27, 133–151 (2021). https://doi.org/10.1007/s10883-020-09487-1

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  • DOI: https://doi.org/10.1007/s10883-020-09487-1

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