Existence, uniqueness and stability of the forced waves and gap formation for Lotka-Volterra competition systems with asymmetric nonlocal dispersal in shifting habitats

This paper is mainly concerned with the Lotka-Volterra competition system with asymmetric nonlocal dispersal in shifting habitats. We first obtain the existence of the forced waves of the Lotka-Volterra competition system by iterative techniques when the shifting wave speed lies in a specific interval, and further find that the gap formations exist if the forced speed exceeds the interval. Moreover, by constructing suitable upper and lower solutions and carefully applying a sliding technique together with some delicate analysis, we establish the uniqueness of the forced wave. Finally, we derive the global stability of the forced wave by the squeeze technique. Our results show that the asymmetric dispersal kernel has an effect on the shifting speed, but only on the location of the interval for the existence of the forced wave and gap formation.