Boundedness And Blow-up Of Solutions To An Attraction-repulsion Chemotaxis System

In this paper,we study the attraction-repulsion chemotaxis system:(?)with a bounded domain ?(?)RN,?,??0,?,?,?,?>0.It was known that the solutions are globally bounded if ??—??<0[1].Under ??—??>0,we prove that the solutions must be globally bounded whenever the initial mass ??u0(x)dx<4?(??-??),and the finite time blow-up may occur if ??u0(x)dx><4?(??-??).