【摘要】 考虑周期微分系统x·(t)=A(t,x(t-r1))x(t)+f(t,x(t-r2))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,A(t+T,x)=A(t,x),f(t+T,x)=f(t,x),且T>0,r1,r2∈R.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,改进和推广了文[1～4]的相关结果.更多还原

【Abstract】 The existence of periodic solutions of periodic differential system with delay x·（t）=A（t,x（t-r₁））x（t）+f（t,x（t-r₂）） are considered,where （t,x）∈R×Rⁿ,the n×n matrix A（t,x） is continuous,the n-vector f（t,x） is continuous,A（t+T,x）=A（t,x）,f（t+T,x）=f（t,x）,and T>0,r₁,r₂∈R.Some sufficient conditions to guarantee the existence of T-periodic solution for the system are established,the related results in are improved and extended.更多还原