Dynamic equations on time scales and generalized ordinary differential equations

Abstract

The aim of this paper is to show that dynamic equations on time scales can be treated in the framework of generalized ordinary differential equations as introduced by J. Kurzweil.

We also use some known results for generalized ordinary differential equations to obtain new theorems related to stability and continuous dependence on parameters for dynamic equations on time scales.

Keywords

• variational stability
• stability with respect to perturbations
• continuous dependence on parameters
• linear equations
• integration on time scales
• Kurzweil–Stieltjes integral