Entire solutions of a diffusive and competitive Lotka–Volterra type system with nonlocal delays

Abstract

This paper is concerned with the entire solution of a diffusive and competitive Lotka–Volterra type system with nonlocal delays. The existence of the entire solution is proved by transforming the system with nonlocal delays to a four-dimensional system without delay and using the comparing argument and the sub-super-solution method. Here an entire solution means a classical solution defined for all space and time variables, which behaves as two wave fronts coming from both sides of the x-axis.