Measure functional differential equations with infinite delay

Abstract

We introduce measure functional differential equations with infinite delay and an axiomatically described phase space. We show how to transform these equations into generalized ordinary differential equations whose solutions take values in a suitable infinite-dimensional Banach space.

Even in the special case of functional equations with finite delay, our result improves the existing one by imposing weaker conditions on the right-hand side.

Keywords

• Measure functional differential equations
• Generalized ordinary differential equations
• Differential equations in Banach spaces
• Regulated functions
• Kurzweil-Stieltjes integral
• Phase space