Entire solutions originating from monotone fronts for nonlocal dispersal equations with bistable nonlinearity

Abstract

This paper mainly focuses on the entire solutions of nonlocal dispersal equations with bistable nonlinearity. Under certain assumptions of wave speed, firstly constructing appropriate super-and sub-solutions and applying corresponding comparison principle, we established the existence and related properties of entire solutions formed by the collision of three and four traveling wave solutions. Then by introducing the definition of terminated sequence, it is proved that there has no entire solutions formed by k traveling wave solutions that collide with each other as long as k ≥ 5. Finally, based on the classical weighted energy approach, we obtain the global exponentially stability of the entire solutions in some weighted space.