Traveling wave solutions of a time-periodic competitive system with a free boundary

We consider a time-periodic competition system with a free boundary, which can be used to describe two species that are struggling on the free boundary to obtain their own habitats and the final competition result is the regional partition of two species. In [15], we have studied the (classical) traveling wave solutions of the temporal homogeneous problems. In this paper, we consider the time-periodic case and study periodic traveling wave solutions of the problem. More precisely, we will prove the existence and uniqueness of the periodic traveling wave solution, and show that the speed of the periodic traveling wave is uniquely determined by and monotonically dependent on the time-periodic terms in the system. Moreover, we will present some sufficient conditions to guarantee that the wave travels with a positive speed.