On positive periodic solutions of a nonautonomous neutral delay n-species competitive system

The purpose of this paper is to investigate a general neutral delay n-species competitive nonautonomous system. Different from Gaines and Mawhin's continuation theorem [R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977] and abstract continuation theory for k-set contraction [W. Petryshyn, Z. Yu, Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems, Nonlinear Anal. 6 (1982) 943-969; R.E. Gaines, J.L. Mawhin, Lecture Notes in Mathematics, vol. 586, Springer-Verlag, Berlin, 1977], a new existence theorem is introduced. With the help of the theorem and some techniques, a set of sufficient conditions are derived for the existence of at least one strictly positive (componentwise) periodic solution. As an application, we also examine some special cases which have been studied extensively in the literature. Some known results are improved and generalized.