Mild solutions for some partial functional integrodifferential equations with finite delay in Fréchet spaces

Mild solutions for some partial functional integrodifferential equations with finite delay in... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

Mild solutions for some partial functional integrodifferential equations with finite delay in Fréchet spaces

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Publisher
Springer Milan
Copyright
Copyright © 2016 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0096-7
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

SeMA JournalSpringer Journals

Published: Oct 11, 2016

References

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