Boundedness of Impulsive Functional Differential Equations via Lyapunov Functional

Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and technology. Recently a well developed stability theory of functional differential systems has come into existence [15-21]. Qualitative properties of impulsive differential equations have been intensively researched for years. In [3-11], by using lyapunov functions and Razumikhin techniques, some Razumikhin type theorems on stability and boundedness are obtained for a class of impulsive functional differential equations. In 1988, Wu [13] presented some sufficient conditions on stability andboundedness of neural functional differential equations with infinite delay using lyapunov functions. The purpose of present paper is to investigate the stability and boundedness theorems for functional differential equations with infinite delays.