Basic results for functional differential and dynamic equations involving impulses

Abstract

We study the relation between measure functional differential equations, impulsive measure functional differential equations, and impulsive functional dynamic equations on time scales. For both types of impulsive equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

Along the way, we also clarify the relation between time scale integrals and Kurzweil-Henstock-Stieltjes integrals.

Keywords

• Impulsive measure functional differential equations
• impulsive functional dynamic equations
• existence and uniqueness
• continuous dependence
• periodic averaging
• Kurzweil-Henstock-Stieltjes integral
• integration on time scales