Stepanov-Like Pseudo Almost Periodic Solutions of Class r in $\alpha$-Norm under the Light of Measure Theory

Issa Zabsonre, Abdel Hamid Gamal Nsangou, Moussa El-Khalil Kpoumie, Salifou Mboutngam

Abstract

The aim of this work is to present some interesting results on  weighted ergodic functions. We also study the existence and uniqueness of $(\mu,\nu)$-weighted Stepanov-like pseudo almost periodic solutions class r for some partial differential equations in a Banach space when the delay is distributed using the spectral decomposition of the phase space developed by Adimy and his co-authors.