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Stepanov pseudo almost periodic functions and applications
  • Kamal Khalil,
  • Marko Kostic,
  • Manuel Pinto
Kamal Khalil
Cadi Ayyad University Faculty of Sciences Semlalia
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Marko Kostic
University of Novi Sad Faculty of Technical Sciences
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Manuel Pinto
Universidad de Chile Facultad de Ciencias Fisicas y Matematicas
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Abstract

In this work, we present basic results and applications of Stepanov pseudo almost periodic functions with measure. Using only the continuity assumption, we prove a new composition result of $\mu$-pseudo almost periodic functions in Stepanov sense. Moreover, we present different applications to semilinear differential equations and inclusions in Banach spaces with weak regular forcing terms. We prove the existence and uniqueness of $\mu$-pseudo almost periodic solutions (in the strong sense) to a class of semilinear fractional inclusions and semilinear evolution equations, respectively, provided that the nonlinear forcing terms are only Stepanov $ \mu $-pseudo almost periodic in the first variable and not a uniformly strict contraction with respect to the second argument. Some examples illustrating our theoretical results are also presented.

Peer review status:UNDER REVIEW

08 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
10 Nov 2020Submission Checks Completed
10 Nov 2020Assigned to Editor
20 Nov 2020Reviewer(s) Assigned
21 Mar 2021Review(s) Completed, Editorial Evaluation Pending
22 Mar 2021Editorial Decision: Revise Major
14 Apr 20211st Revision Received
14 Apr 2021Assigned to Editor
14 Apr 2021Submission Checks Completed
14 Apr 2021Reviewer(s) Assigned
15 Apr 2021Review(s) Completed, Editorial Evaluation Pending
26 Apr 2021Editorial Decision: Revise Major
02 May 20212nd Revision Received
03 May 2021Assigned to Editor
03 May 2021Submission Checks Completed
11 May 2021Reviewer(s) Assigned
13 May 2021Review(s) Completed, Editorial Evaluation Pending