scholarly journals Existence of μ-pseudo almost automorphic solutions to a neutral differential equation by interpolation theory

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 603-614 ◽  
Author(s):  
Yong-Kui Chang ◽  
Xiao-Xia Luo
Keyword(s):  
Differential Equation ◽  
Existence Results ◽  
Neutral Differential Equation ◽  
Interpolation Theory ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Automorphic ◽  
Fixed Point Methods ◽  
Automorphic Functions ◽  
Composition Theorem

In this paper, we shall deal with ?-pseudo almost automorphic solutions to a neutral differential equation. To achieve this goal, we first prove a composition theorem for ?-pseudo almost automorphic functions under suitable conditions, and then apply it to investigate some existence results by the interpolation theory and fixed point methods.

scholarly journals Pseudo Almost Automorphic Solutions for Differential Equations Involving Reflection of the Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Elhadi Ait Dads ◽  
Samir Fatajou ◽  
Lahcen Khachimi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Exponential Dichotomy ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Automorphic ◽  
Fixed Point Methods ◽  
Automorphic Functions

By means of the fixed point methods and the properties of the pseudo almost automorphic functions, the existence and uniqueness of pseudo almost automorphic solutions are obtained for differential equations involving reflection of the argument. For the nonscalar, case we use the exponential dichotomy properties.

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.

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