scholarly journals Pseudo almost automorphic solutions of class r in α-norm under the light of measure theory

2020 ◽  
Vol 7 (1) ◽  
pp. 81-101
Author(s):  
Issa Zabsonre ◽  
Djendode Mbainadji
Keyword(s):  
Phase Space ◽  
Spectral Decomposition ◽  
Measure Theory ◽  
New Approach ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Automorphic ◽  
Automorphic Functions

AbstractUsing the spectral decomposition of the phase space developed in Adimy and co-authors, we present a new approach to study weighted pseudo almost automorphic functions in the α-norm using the measure theory.

(μ, ν)-Pseudo almost automorphic solutions for some non-autonomous differential equations

2015 ◽  
Vol 26 (11) ◽  
pp. 1550090 ◽  
Author(s):  
El Hadi Ait Dads ◽  
Khalil Ezzinbi ◽  
Mohsen Miraoui
Keyword(s):  
Differential Equations ◽  
Exponential Dichotomy ◽  
Linear Part ◽  
Nonlinear Part ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Automorphic ◽  
Autonomous Differential Equations ◽  
Automorphic Functions

The aim of this work is to study the new concept of the (μ, ν)-pseudo almost automorphic functions for some non-autonomous differential equations. We suppose that the linear part has an exponential dichotomy. The nonlinear part is assumed to be (μ, ν)-pseudo almost automorphic. We show some results regarding the completness and the invariance of the space consisting in (μ, ν)-pseudo almost automorphic functions. Then we propose to study the existence of (μ, ν)-pseudo almost automorphic solutions for some differential equations involving reflection of the argument.

On Stepanov-like (pseudo) almost automorphic functions

2011 ◽  
Vol 74 (8) ◽  
pp. 2853-2861 ◽  
Author(s):  
Zhenbin Fan ◽  
Jin Liang ◽  
Ti-Jun Xiao
Keyword(s):  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Automorphic ◽  
Automorphic Functions
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