Differentiability of Solutions with Respect to the Initial Data in Differential Equations with State-dependent Delays
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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.
KeywordsDelay differential equation State-dependent delay Differentiability with respect to parameters
Mathematics Subject Classification (2000)34K05
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- 3.Coddington E.A., Levinson N.: Theory of Ordinary Differential Equations. Robert E. Krieger Publishing Company, Malabar, FL (1984)Google Scholar
- 6.Hartung, F.: On classes of functional differential equations with state-dependent delays. Ph.D. Dissertation, University of Texas at Dallas, Richardson, TX, USA (1995)Google Scholar
- 9.Hartung F., Krisztin T., Walther H.O., Wu J.: Functional differential equations with state-dependent delays: theory and applications. In: Cañada, A., Drábek, P., Fonda, A. (eds) Handbook of Differential Equations: Ordinary Differential Equations, pp. 435–545. Elsevier, North-Holand (2006)CrossRefGoogle Scholar
- 13.Walther, H.O.: Smoothness properties of semiflows for differential equations with state dependent delay. Russian, In: Proceedings of the International Conference on Differential and Functional Differential Equations, Moscow, 2002, vol. 1, pp. 40–55, Moscow State Aviation Institute (MAI), Moscow 2003. English version: J. Math. Sci. 124, 5193–5207 (2004)Google Scholar