具分布时滞的一类Logistic方程的周期正解

摘要

利用重合度定理,建立了下面具分布时滞的Logistic方程x'(t)=x(t)∑ni=1ri(t)1-(1)/(K(t))∫t-∞x(s)dsRi(t,s)正周期存在的充分条件.其中ri(t),K(t)和Ri(t,s)是以ω＞0为周期的正周期函数.%With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,the global existence of positive periodic solutions of the following logistic equaiton with distributed delays are established x'(t)=x(t)∑ni=1ri(t)1-(1)/(K(t))∫t-∞x(s)dsRi(t,s) where ri(t),K(t) and Ri(t,s) are positive periodic continuous functions with periodic ω＞0.