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Identification of parameters in delay equations with state-dependent delays. (English) Zbl 0894.34071

The authors study existence principles for integral equations of Volterra type in \(\mathbb{R}^n\). By fixed point methods existence is obtained for the general equation \(y'(t)= Vy(t)\), \(t\geq 0\), \(y(0)= y_0\). The mapping \(V\) (of Volterra type) maps \(L^p[0, T]\) into \(L^{p'}[0, T]\) continuously and satisfies certain technical assumptions (too lengthy to be included here). Applications to the cases where \(Vy= f(t,y(t), \int^t_0 k(t,s,y(s))ds)\) and \(Vy= h(t)+ \int^t_0 k(t,s)g(s,y(s))ds\) are considered in detail.
Reviewer: S.O.Londen (Espoo)

MSC:

34K35 Control problems for functional-differential equations
34K05 General theory of functional-differential equations
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