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On differentiability of solutions with respect to parameters in state-dependent delay equations. (English) Zbl 0877.34045
The author studies differentiability of solutions of the state-dependent delay system \[ \dot x(t)= f(t,x(t),x(t-\tau(t,x_t,\sigma)), \theta),\quad t\in[0,T] \] with initial conditions \(x(t)=\varphi(t)\), \(t\in[-r,0]\) with respect to the parameters of the equation.
Sufficient conditions for differentiability of the \(W^{1,p}\) norm \((1\leq p<\infty)\) are given. In the proof of the main results, the author uses an extention of the uniform contradiction principle to quasi-Banach spaces.

34K05 General theory of functional-differential equations
34K30 Functional-differential equations in abstract spaces
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
Full Text: DOI
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