In this work, we study the existence of mild solutions for some partial functional integrodifferential equations with finite delay in a Fréchet spaces. We assume that the linear part has a resolvent operator in the sense given by Grimmer (Trans Am Math Soc 273: 333–349, 1982). The nonlinear part is a sum of a Lipschitzian function and another satisfies the Carathéodory’s conditions. Our approach is based on a nonlinear alternative of Avramescu type and the resolvent operators theory. An application is provided to a reaction-diffusion equation with delay.
SeMA Journal – Springer Journals
Published: Oct 11, 2016
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