| Impulsive differential equations can fully consider the impact of instantaneous things on the development of the entire thing,and can more accurately reflect the es-sential laws of things change.Therefore,the study of impulsive differential equations has more important significance.This article uses impulsive analysis techniques to study the C1-smoothness of the solution manifold and continuous semiflow produced by its continuously differentiable solution of the following two types of initial value problem for impulsive differential equations with state-dependent delay (?)and(?) respectively.Firstly,when the nonlinear function and the delay term are Lipschitz contin-uous,the neutral function is C1-continuous,we discuss the C1-smoothness of the solution manifold for the problem(1)in the real space.Secondly,based on the continuous differentiability of the solution manifold of the problem(1),we use the impulsive analysis technique to estimate the growth of the solution,thereby ob-tain the C1-smoothness of the continuous semi-flow generated by the solution of the problem(1).Thirdly,by using the properties of compact semigroups and the Holder continuity of linear function,we study the C1-smoothness of the solution manifold of the initial value problem(2)of the abstract impulsive evolution equation with delay in Banach space.Fourthly,by using the boundness of compact semigroups and impulsive analysis techniques,a new growth estimate of the continuous differen-tiable solution is obtained,and then the continuous differentiability of the solution semiflow of the problem(2)is proved. |
