时滞泛函微分方程的某些稳定性定理

Some stability theorems for retarded functional differential equations

给出了时滞泛函微分方程的本解一致稳定性的新判据，V的上界可以是某些条件下的正函数；对于解的渐近性及渐近稳定性和一致渐近稳定性结出的判据，去掉了方程右端函数f的有界性假设，使V的上界容许是在某种条件下的常负函数，推广了J.KHale的结果，便于应用．

In this paper, the authors investlgate uniform stability, asymptotic stability,and uniforrn asymptotic stability for the zero solution of retarded functional differential equations. Some well-known results for unlform stability, in which the derivative of Lyapunov functional V is required to be posltlve semi-definite, are generalized. The upper bound of V is allowed to be positive function under some conditions. The assumption of boundness for f(t,x1,) has been removed, and the upper bound of V is allowed to be negative semi-definite under some conditions for the study of asymptotic stability.