Differentiability of Solutions with Respect to the Initial Data in Differential Equations with State-dependent Delays

• Published in: Journal of dynamics and differential equations Vol. 23; no. 4; pp. 843 - 884
• Main Author: Hartung, Ferenc
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2011
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Differentiability with respect to parameters; 34K05; State-dependent delay; Delay differential equation

In this paper we consider a class of differential equations with state-dependent delays. We show differentiability of the solution with respect to the initial function and the initial time for each fixed time value assuming that the state-dependent time lag function is strictly monotone increasing.