关键词: 周期正解, 抽象连续定理, 中立型泛函微分方程, k集压缩算子

Abstract:

In this paper, the authors employ an abstract continuous theorem of kset  contractive operator and some analysis techniques to study the existenceof positive periodic  solutions for a neutral functional differential equationas follows[SX(]dN[]dt[SX)]=N(t)［a(t)-β(t)N(t)-∑[DD(]n[]j=1[DD)]b\-j(t) N(t-σ\-i(t))-∑[DD(]m[]i=1[DD)]c\-i(t)N′(t-τ\-i(t))］.Some new results on the existence of positive periodic solutions are obtained.
The  results extend and generalize the corresponding work of  known  literature.

Key words: Positive periodic solution, Abstract continuous , theorem; , Neutral functional differential equation; , kset contractive operator