Linear measure functional differential equations with infinite delay

Abstrakt

We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions.

Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

Klíčová slova

• Measure functional differential equations
• generalized ordinary differential equations
• Kurzweil-Stieltjes integral
• impulsive functional differential equations
• infinite delay
• existence and uniqueness
• continuous dependence