具有变量时滞的高维周期系统的周期解

考虑高维周期系统x·(t) =A(t,x(t-r1(t) ) )x(t) +f(t,x(t-r2 (t) ) )的T -周期解的存在性问题 ,其中 (t,x)∈R×Rn,A(t,x)是n×n连续矩阵函数 ,f(t,x)是n维连续向量函数 ,时滞ri(t) (i=1,2 )是连续函数 ,且A(t+T ,x) =A(t,x) ,f(t+T ,x) =f(t,x) ,ri(t+T) =ri(t) (i=1,2 ) ,常数T >0 .利用不动点方法 ,建立了保证系统存在T -周期解的充分条件 。

一类具偏差变元的高维周期系统的周期解

探研下面具偏差变元的高维周期系统的周期解的存在性、唯一性、稳定性等问题。这里，是n阶实连续的函数方阵，且，(为常数)。是上的n维连续函数，且对任意的，，r为实参数，利用指数型二分性和不动点方法，推广了文[1]的主要结果。

一类具有时滞的微分系统的周期解

研究一类具有分布滞量的高维周期微分系统周期解的存在性和唯一性 .利用不动点方法 。

The Existence of Periodic Orbits for Higher Dimensional Autonomous Systemswith Small Perturbations

By means of theory of toplogical degree in nonlinear functional analysis combining with qualitative analysis method in ordinary differential equations, we discuss the existence of nontrivial periodic orbits for higher dimensional autonomous system with small perturbations.

The Existence of Periodic Orbits to a Higher Dimensional Autonomous System with aNon-hyperbolic Singular Point *

By means of theory of topological degree in nonlinear functional analysiscombining with qualitative analysis in ordinary differential equations, we discuss theexistence of nontrivial periodic orbits to a higher dimensional autonomous system witha non-hyperbolic singular point.