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Existence results for partial neutral functional differential equations with unbounded delay. (English) Zbl 0915.35110
The authors prove existence of mild solutions of the Cauchy problem $${d\over dt} (x(t)+ F(t, x_t))= Ax(t)+ G(t, x_t),\quad t\ge\sigma,\quad x(\sigma)= \varphi\in \Omega,\tag 1$$ where $\Omega$ is an open subset of the phase space, $F,G: [0,a]\times \Omega\mapsto X$ are continuous functions, $0\le\sigma< a$ and $A$ is the infinitesimal generator of an analytic semigroup $T(.)$ of bounded linear operators on $X$. In the case $\sigma= 0$ the existence of strong solutions of the Cauchy problem (1) is proved.
Reviewer: D.Bainov (Sofia)

MSC:
35R10Partial functional-differential equations
34K40Neutral functional-differential equations
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References:
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