scholarly journals Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Abdelkarim-Nidal Akdad ◽  
Khalil Ezzinbi ◽  
Lotti Souden
Keyword(s):  
Existence Result ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic ◽  
Automorphic Functions

AbstractIn this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.

scholarly journals Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations

2020 ◽  
Vol 7 (1) ◽  
pp. 32-52
Author(s):  
Fritz Mbounja Béssémè ◽  
David Békollè ◽  
Khalil Ezzinbi ◽  
Samir Fatajou ◽  
Duplex Elvis Houpa Danga
Keyword(s):  
Integral Equations ◽  
Evolution Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Convolution Product ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic

AbstractThe aim of this work is to give sufficient conditions ensuring that the space PAP(𝕉, X, µ) of µ-pseudo almost periodic functions and the space PAA(𝕉, X, µ) of µ-pseudo almost automorphic functions are invariant by the convolution product f = k * f, k ∈ L1(𝕉). These results establish sufficient assumptions on k and the measure µ. As a consequence, we investigate the existence and uniqueness of µ-pseudo almost periodic solutions and µ-pseudo almost automorphic solutions for some abstract integral equations, evolution equations and partial functional differential equations.

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