Measure functional differential equations and functional dynamic equations on time scales

Abstract

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations.

For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

Keywords

• Measure functional differential equations
• functional dynamic equations
• generalized ordinary differential equations
• existence and uniqueness
• continuous dependence on a parameter
• periodic averaging