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Stepanov-like pseudo almost periodic solutions
of infinite class under the light of measure theory

Issa ZABSONRE(1) and Djokata VOTSIA (2)
Université Joseph KI-ZERBO,
Unité de Recherche et de Formation en Sciences Exactes
et Appliquées, Département de Mathématiques
B.P.7021 Ouagadougou 03, Burkina Faso

Mathematics Subject Classification: (MSC 2010) 34K30; 35B15; 35K57; 44A35; 42A85; 42A75
Key words : measure theory; ergodicity; Weighted Stepanov-like pseudo almost periodic function; evolution equations; partial functional differential equations; infinite delay. 


The aim of this work is to study weighted Stepanov-like pseudo almost periodic functions with infinite delay 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 (μ,ν)-Weighted Stepanov-like pseudo almost periodic solutions of infinite class for some neutral partial functional differential equations in a Banach space with infinite delay.

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