Monotone Iterative Technique for Impulsive Differential-Difference Equations with Variable Impulsive Perturbations

This paper deals with impulsive differential-difference equations for which the impulses are realized at moments when the integral curve of the initial value problem considered meets fixed curves in the extended phase space of the equation. The corresponding impulsive differential-difference inequalities are considered. Sufficient conditions are given for the absence of the phenomenon “beating” and for the continuation of the solutions of the initial value problems for impulsive differential-difference equations and inequalities. Monotone sequences of lower and upper solutions of the initial value problem for the impulsive differential-difference equations are constructed. Under some natural assumptions it is proved that these sequences are convergent to the solutions of the same problem. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.