摘要
讨论一类微分差分方程 x(t) =gradG(x(t) ) +f(t,x(t-r) )的周期解问题 ,其中x(t) =(x1(t) ,… ,xn(t) ) T 是n维连续向量 ,G(x)为连续可微函数 ,r>0 ,f(t,x)是n维连续向量函数 ,且f(t+ω ,x) =f(t,x) ,ω>0。利用重合度理论中的延拓定理并构造Lyapunov泛函得到了周期解的存在性和全局吸引性定理。改进并扩充了文 [3]的有关结果。
The problem of periodic solutions to the following differential difference equations = grad G(x(t))+f(t,x(t-r)) was discussed,where x(t)=(x 1(t),…,x n(t)) T was continuous vector, G(x) was a continuous differential function, f(t,x) was continuous vector function,and f(t+ω,x)=f(t,x),ω>0,r>0 .By using continuation theorem in coincidence degree theory and constructing Lyapunov functional,some theorems on the existence and global attractivity of periodic solutions were obtained.These results in this paper improved and enlarged related result in [3].
