Mild solutions for some partial functional integrodifferential equations with state-dependent delay
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2017, Vol 37, Issue 2
Abstract
In this work, we establish sufficient conditions for the existence of solutions for some partial functional integrodifferential equations with state-dependent delay. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in Banach space, Transaction of American Mathematical Society 273 (1982) 333--349]. The delayed part is assumed to satisfy Caratheodory's conditions. Our approach is based on a nonlinear alternative of Leray-Schauder type and the resolvent operators theory. An application is provided to a reaction-diffusion equation with state-dependent delay.
Authors and Affiliations
Mohamed Alia, Khalil Ezzinbi, Sylvain Koumla
Keywords
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- EP ID EP481682
- DOI 10.7151/dmdico.1197
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