Periodic averaging theorems for various types of equations

Abstract

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.

Keywords

• periodic averaging
• generalized ordinary differential equations
• ordinary differential equations with impulses
• dynamic equations on time scales
• retarded functional differential equations
• retarded difference equations