Front-like Entire Solutions for a Lotka-Volterra Weak Competition System with Nonlocal Dispersal

This paper is concerned with the front-like entire solutions for a Lotka-Volterra weak competition system with nonlocal dispersal. Here, an entire solution means a classical solution defined for all space and time variables. This system has traveling wavefronts and enjoys the comparison principle. Based on these traveling wavefronts, we construct some super- and sub-solutions. Then, by using the comparison principle and the super- and sub-solutions method, we establish the existence of front-like entire solutions which behave as two wavefronts coming from the both sides of x-axis. Moreover, some properties of the front-like entire solutions are obtained.