Existence of positive periodic solutions for a nonautonomous neutral delay n-species competitive model with impulses

In this paper, by using some analysis techniques and a new existence theorem, which is different from Gaines and Mawhin’s continuation theorem and abstract continuation theory for k-set contraction, we obtain some sufficient and realistic conditions for the existence of positive periodic solution of a general neutral delay n-species competitive model with impulses. As an application, we also examine some special cases which have been studied extensively in the literature. Some known results are improved and generalized.