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On the integro-differential equations with reflection
  • El Hadi Ait Dads,
  • Safoua Khelifi,
  • Mohsen MIRAOUI
El Hadi Ait Dads
Université Cadi Ayyad, Faculté des Sciences Semlalia B.P. 2390
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Safoua Khelifi
Université de Sfax Faculté des Sciences de Sfax
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Mohsen MIRAOUI
IPEI of Kairouan
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Abstract

There are a few purely periodic phenomena in nature, which allows one to consider several other generalizations, such as almost automorphic and measure pseudo almost automorphic oscillations. 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.

Peer review status:ACCEPTED

29 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
02 May 2020Submission Checks Completed
02 May 2020Assigned to Editor
18 May 2020Reviewer(s) Assigned
18 Jun 2020Review(s) Completed, Editorial Evaluation Pending
22 Jun 2020Editorial Decision: Revise Minor
23 Jun 20201st Revision Received
24 Jun 2020Submission Checks Completed
24 Jun 2020Assigned to Editor
24 Jun 2020Editorial Decision: Accept