On the integro-differential equations with reflection |
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Authors: | Elhadi Ait Dads Safoua Khelifi Mohsen Miraoui |
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Institution: | 1. Cadi Ayyad University, Morocco, UMI 209 UMMISCO, IRD 2. Bondy France, Unité Associée au CNRST URAC 02, Morocco;3. LR11ES53, University of Sfax, Sfax, Tunisia;4. University of Kairouan, LR11ES53, University of Sfax, Sfax, Tunisia |
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Abstract: | In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed-point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general-type reflection integro-differential equations. We suppose that the nonlinear part is measure pseudo almost automorphic and in which we distinguish the two constant and variable cases for the Lipschitz coefficients of the functions associated with this part. It is assumed that the linear part of the equation considered admits an exponential dichotomy. Finally, an application is given on the very interesting model of Markus and Yamabe. |
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Keywords: | exponential dichotomy integro-differential equations pseudo-almost automorphic reflection |
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