Generalized differential equations: Differentiability of solutions with respect to initial conditions and parameters

Abstract

We show that under certain assumptions, solutions of generalized ordinary differential equations are differentiable with respect to initial conditions and parameters. This result unifies and extends several existing theorems for other types of equations, such as impulsive differential equations or dynamic equations on time scales.

Keywords

• Generalized ordinary differential equations
• Differentiability of solutions
• Kurzweil integral
• Differential equations with impulses
• Dynamic equations on time scales