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The Kneser property for abstract retarded functional differential equations with infinite delay. (English) Zbl 1029.34065
The author deals with semilinear abstract retarded functional-differential equations (ARFDEs) with infinite delay $x'(t)= Ax(t)+ f(t, x_t),\quad 0\leq t\leq\tau,\quad x_0= \varphi\in\Phi,$ where $$A$$ is the infinitesimal generator of a strongly continuous semigroup on a Banach space $$X$$ and $$\Phi$$ is the phase space for the equation.
He establishes the existence of mild solutions to ARFDEs and proves that the set of mild solutions is connected in the space of continuous functions. An application to population models is given.

##### MSC:
 34K30 Functional-differential equations in abstract spaces 92D25 Population dynamics (general)
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