Abstract
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].
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