Continuous dependence on initial values for impulsive delay differential equations. (Q1764544)

This paper studies the continuous dependence of solutions with repect to initial values for the impulsive delay differential system \[ x'(t)=f(t,x_t),\;\;t\not=\tau_k, \] \[ \Delta x(t)=I(t,x_t,\;t=\tau_k, \] with \(0=\tau_0<\tau_1<\cdots, \) and \(\lim_{k\rightarrow +\infty}\tau_k=+\infty\). Under some assumptions, the authors prove that the solutions depend continuously on the initial function.