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Francis K. A. Allotey (Saltpond, Ghana 9 August 1932 – Accra, Ghana 2 November 2017) Read chapter Read first chapter

2019 | OriginalPaper | Chapter

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

Authors : Hamidou Toure, Issa Zabsonre

Published in: Analysis and Partial Differential Equations: Perspectives from Developing Countries

Publisher: Springer International Publishing

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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.

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previous chapter Well-posed Boundary Value Problems for New Classes of Singular Integral Equations in Cylindrical Domains
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Metadata
Title
Weighted Stepanov-Like Pseudo Almost Automorphic Solutions of Class r for Some Partial Differential Equations
Authors
Hamidou Toure
Issa Zabsonre
Copyright Year
2019
Book
Analysis and Partial Differential Equations: Perspectives from Developing Countries

Print ISBN: 978-3-030-05656-8

Electronic ISBN: 978-3-030-05657-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-05657-5_15

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