Abstract
The aim of this work is to present new approach to study weighted pseudo almost periodic and automorphic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions. We study the existence and uniqueness of \(\mu \)-pseudo almost periodic and automorphic solutions of class r for some neutral partial functional differential equations in a Banach space when the delay is distributed using the spectral decomposition of the phase space developed in Adimy and co-authors. Here we assume that the undelayed part is not necessarily densely defined and satisfies the well-known Hille–Yosida condition, the delayed part are assumed to be pseudo almost periodic or pseudo almost automorphic with respect to the first argument and Lipschitz continuous with respect to the second argument.
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Acknowledgements
The authors would like to thank the referees for their careful reading of this article. Their valuable suggestions and critical remarks made numerous improvements throughout this article and which can help for future works. He also would like to thank LAMI (Laboratoire de Mathématiques et d’Informatique) in Burkina Faso and LMDP (Laboratoire de Mathématiques et Dynamique de Population) in Morroco to support this work.
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Ezzinbi, K., Toure, H. & Zabsonre, I. Weighted Pseudo Almost Periodic and Pseudo Almost Automorphic Solutions of Class r for Some Partial Differential Equations. Differ Equ Dyn Syst 29, 313–338 (2021). https://doi.org/10.1007/s12591-018-00447-7
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DOI: https://doi.org/10.1007/s12591-018-00447-7
Keywords
- Measure theory
- Ergodicity
- \(\mu \)-pseudo almost periodic and automorphic functions
- Evolution equations
- Reaction diffusion system
- Partial functional differential equations