Traveling wave solutions in a reaction–diffusion competition-cooperation system with stage structure

  • Kun LiEmail author
  • Xiong Li
Original Paper Area 1


In this paper we establish the existence of traveling wave solutions in a reaction–diffusion system for two species with stage structure by using Schauder’s fixed point theorem and the iteration scheme. In order to illustrate our results, we choose four different kernels to apply to this system, the verification of upper and lower solutions is very nontrivial due to asymmetric nonlinear terms. The effects of delays and the diffusivity of the immature and mature species on the lower bound of the wave speed are also investigated.


Reaction–diffusion system Traveling wave solution Stage structure Upper and lower solutions Nonlocal delay 

Mathematics Subject Classification

35R20 34K10 35K57 


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK 2017

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceHunan First Normal UniversityChangshaPeople’s Republic of China
  2. 2.School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of EducationBeijingPeople’s Republic of China

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