PERIODIC SOLUTIONS OF PLANAR SYSTEM WITH SIX DELAYS

In this paper we obtain some sufficient conditions for the existence of non-constant periodic solutions of the following planar system with six delaysOur approach is based on the continuation theorem of the coincidence degree.     

多物种竞争差分系统正周期解的存在性

本利用Mawhin的重合度理论研究了一类多物种竞争差分系统正周期解的存在性，获得了保证该差分系统存在正周期解的新的充分条件．     

具有连续变量的差分方程振动性的判据

借助研究离散变量的差分方程振动性的一般方法,本文建立了具有连续变量、变系数的差分方程振动性判据,其结果改进了文献［４］中的一些结果．     

THE EXISTENCE OF POSITIVE PERIODIC SOLUTIONS IN A LOGISTIC DIFFERENCE MODEL WITH A FEEDBACK CONTROL

Consider the following nonautonomous delayed periodic logistic difference model with feedback control termwhich describes the evolution of a single species. The existence of a positive periodic solution is established by using the method of Mawhin's coincidence degree. This work has important significance in both theory and applications.     

二阶中立型差分方程的振动性与渐近性

考虑二阶中立型差分方程 △~２（ｘ_ｎ－ｃｘ_（ｎ－ｒ）＋∑ｑ_（ｉ,ｎ）ｘ_（ｎ－σ_ｉ）＝０（ｎ＝０,１,２,…） （１）当 Ｃ＞０时我们得到了方程的所有解振动或非振动解趋于零的若干充分条件,本文的结果推广了文［２］中的结果．     

具变时滞差分方程解的振动性

本文研究了一类具变时滞的非线性差分方程解的振动性,获得了该方程解的振动准则．将结论应用于差分方程ΔＸｎ ＋ ｐｎｘｎ－ ｋｎ ＝ ０　　ｎ ＝ ０,１,２,… （）其中ｐｎ≥０,｛ｋｎ｝是正整数数列且ｌｉｍｎ→∞｛ｎ－ ｋｎ｝＝ ∞．我们得到了方程（）振动的新的充分条件．     

THE EXISTENCE OF PERIODIC SOLUTIONS AND GLOBAL ATTRACTIVITY OF A CONTINUOUS MODEL OF BOBWHITE QUAIL

The existence of a positive periodic solution foru'(t) =u(t)[α(t)-1+β(t)/1+uk(t-τ(t))], t≥0is established. Some sufficient conditions are obtained for the periodic solution to be globally attractive.     

具正负系数中立型时滞差分方程解的振动性

本文讨论一阶具正负系数中立型时滞差分方程 △（ｘ（ｎ）－ｃ（ｎ）ｘ（ｎ－ｋ））＋ｐ（ｎ）ｘ（ｎ－ｍ）－Ｑ（ｎ）ｘ（ｎ－１）－０,ｎ＝０,１,２,…我们获得了使方程所有解振动的“ｓｈａｒｐ”条件,即在系数ｐ（ｎ）,Ｑ（ｎ）,Ｃ（ｎ）为常数时是充分必要条件,本文的结果推广并改进了已有的结果．