Existence of positive periodic solution of mutualism system with several delays

In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solutions of a mutualism systems with bounded and unbounded delays. Our results generalize significantly improve those of Gopalsamy and He [Gopalsamy K, He XZ. Persistence, attractivity, and delay in facultative mutualism. J Math Anal Appl 1997;215:154–73], Yang et al. [Yang F, Jiang D, Ying A. Existence of positive solution of multidelays facultative mutualism system. J Eng Math 2002;3:64–8], Chen et al. [Chen FD, Shi JL, Chen XX. Periodicity in Lotka–Volterra facultative mutualism system with several delays. J Eng Math 2004;21(3)] and Xia and Lin [Xia YH, Lin M, Existence of positive periodic solution of mutualism system with infinite delays. Ann Diff Eqs 2005;21(3):448–53].