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Weighted Stepanov-Like Pseudo Almost Automorphic Solutions of Class r for Some Partial Differential Equations

  • Hamidou ToureEmail author
  • Issa Zabsonre
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)

Abstract

The aim of this work is to study weighted Stepanov-like pseudo almost 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 also study the existence and uniqueness of \((\mu ,\nu )\) -Weighted Stepanov-like pseudo almost 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 by 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 automorphic with respect to the first argument and Lipschitz continuous with respect to the second argument.

Keywords

Automorphic solutions Pseudo periodic functions Lipschitz condition 

Notes

Acknowledgement

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.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Département de MathématiquesUniversité de Ouaga 1 Pr Joseph Ki-ZerboOuagadougou 03Burkina Faso

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