Traveling wave solutions of a nonlocal dispersal predator–prey model with spatiotemporal delay

Abstract

In this paper, we study the existence and nonexistence of traveling wave solution for the nonlocal dispersal predator–prey model with spatiotemporal delay. This model incorporates the Leslie–Gower functional response into the Lotka–Volterra-type system, and both species obey the logistic growth. We explore the existence of traveling wave solution for $$c\ge c^{\star }$$ by using the upper-lower solutions and the Schauder’s fixed point theorem. Furthermore, the nonexistence of traveling wave solution for $$c<c^{\star }$$ is discussed by means of the comparison principle. The novelty of this work lies in the construction of upper-lower solutions and the proof of the complete continuity of operator.