Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 55, pp. 1-15.

Title: Traveling wave solutions for three-species nonlocal competitive-cooperative systems
       
Authors: Hong-Jie Wu    (Southwest Jiaotong Univ., Chengdu, Sichuan China)
         Bang-Sheng Han (Southwest Jiaotong Univ., Chengdu, Sichuan China)
         Shao-Yue Mi    (Southwest Jiaotong Univ., Chengdu, Sichuan China)
         Liang-Bin Shen (Southwest Jiaotong Univ., Chengdu, Sichuan China)
         
Abstract: 
By using a two-point boundary-value problem and a Schauder's fixed point
theorem, we obtain traveling wave solutions connecting $(0,0,0)$
to an unknown positive steady state for speed
$c\geq c^{\ast}=\max\{2,2\sqrt{d_2r_2},2\sqrt{d_3r_3}\}$.
Then we present some asymptotic behaviors of traveling wave solutions.
In particular we show that the nonlocal effects have a great influence on
the final state of traveling wave solutions at $-\infty$.

Submitted April 6, 2023. Published September 04, 2023.
Math Subject Classifications: 35A01, 35C07, 35K55, 35K57.
Key Words: Three-species system; competitive-cooperative; nonlocal effect; traveling wave solution; critical speed.