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Linearizing equations with state-dependent delays. (English) Zbl 0694.34050
Let \(T_{f,r}: W^{1,\infty}[a,b]\to L^ p[a,b]\), \(1\leq p<\infty\) be given by the formula \([T_{f,r}(x)](t)=f(t,x(r(t,x(t)))),\) \(t\in [a,b]\) where \(f,r:[a,b]\times {\mathbb{R}}\times {\mathbb{R}}\to {\mathbb{R}}.\) The authors give sufficient conditions of differentiability of \(T_{f,r}\) at the arbitrary point \(X^ 0\in W^{1,\infty}[a,b]\).
Reviewer: R.R.Akhmerov

34K05 General theory of functional-differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text: DOI
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