Existence and uniqueness results for impulsive delay differential equations. (English) Zbl 0955.34068

Ballinger, George; Liu, Xinzhi

Dyn. Contin. Discrete Impulsive Syst. 5, No. 1-4, 579-591 (1999).

The authors establish existence and uniqueness results for a general class of impulsive differential equations of the form \[ x'(t)= f(t,x_t),\quad t\geq t_0,\quad \Delta x(t)= I(t, x_{t^-}),\quad t=\tau_k,\quad t> t_0. \] In addition, a discussion of these problems is presented.

Reviewer: Stieg Olof Londen (Espoo)

MSC:

34K45

Functional-differential equations with impulses

Keywords:

impulsive differential equations; existence; uniqueness