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.
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.
Reviewer: P.Marušiak (Žilina)
MSC:
| 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) |
Keywords:
delay differential systems; state-dependent delay system; uniform contradiction principle; quasi-Banach spacesReferences:
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