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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

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