Existence of solutions for some nonautonomous partial functional differential equations with state-dependent delay

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Résumé

The aim of this work is to prove the existence of mild solutions for some nondensely nonautonomous partial functional diferential equations with state-dependent delay in Banach spaces. We assume that the linear part is not necessarily densely deined and generates an evolution family. Our approach is based on a nonlinear alternative of Leray-Schauder type and nonautonomous evolution family with nondensely domain. We propose a reaction difusion equation with state-dependent delay to illustrate the obtained result.

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