Time periodic traveling fronts of pyramidal shapes for periodic Lotka-Volterra competition-diffusion system

This paper is concerned with the time periodic traveling front solutions of pyramidal shapes for time periodic Lotka-Volterra competition-diffusion system in RN with N≥3. It should be mentioned that the existence, uniqueness and stability of two-dimensional time periodic traveling curved fronts of time periodic Lotka-Volterra competition-diffusion system in R2 have been studied yet. By the supersolution and subsolution technique coupled with comparison principle, in this paper we construct the existence, non-existence and qualitative properties of time periodic pyramidal traveling front solutions for time periodic Lotka-Volterra competition-diffusion system in RN.