Boundedness and partial survival of species in nonautonomous Lotka-Volterra systems

This paper generalizes results of the well-known May-Leonard system and the recent work of Redheffer (Nonlinear Anal.: Real World Appl. 4 (2003) 301) to the above nonautonomous Lotka-Volterra systems with delays. We establish conditions of the boundedness and partial survival for the solution x(t)=[xi(t)] of system in the sence that max1⩽i⩽nxi(t) is bounded away from 0 even though inft⩾t0xi(t)=0 for some i.