滞后型脉冲泛函微分方程解对初值的可微性

Differentiability in Terms of Initial Value for Impulsive Functional Differential Equation

考虑脉冲泛函微分方程{x′=f(t,xt),t>t0,t≠tk,△x=Ik(x(t)),t=tk,k=1,2,…,x(t0+)=ω,xt0=φ。局部解的存在性,及在局部解存在的前提下解对初值(φ,f)的可微性。

Consider impulsive functional differential equation {x^1=f（t,xt）,t〉t0,t≠tk;△x=Ik（x（t））,t=tk,k=1,2……;x（t^＋0）=ω;xt0=φ the existence of local solution and dierentiability of solution about initial value on condition is studied that the exist-ence of local solution.