scholarly journals Discrete Weighted Pseudo Almost Automorphic Solutions of Nonautonomous Difference Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Xiaoqing Wen ◽  
Hongwei Yin
Keyword(s):  
Difference Equations ◽  
Automorphic Function ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Pseudo Almost Automorphic

We introduce the concept of a discrete weighted pseudo almost automorphic function and prove some basic results. Further, we investigate the nonautonomous linear and semilinear difference equations and obtain the weighted pseudo almost automorphic solutions of both these kinds of difference equations, respectively. Our results generalize the ones by Lizama and Mesquita (2013).

Weighted pseudo δ-almost automorphic functions and abstract dynamic equations

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan
Keyword(s):  
Time Scales ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Automorphic Function ◽  
Dynamic Equations ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Automorphic Functions

Abstract In this paper, we propose the concept of a weighted pseudo δ-almost automorphic function under the matched space for time scales and we present some properties. Also, we obtain sufficient conditions for the existence of weighted pseudo δ-almost automorphic mild solutions to a class of semilinear dynamic equations under the matched spaces for time scales.

scholarly journals Discrete Weighted Pseudo-Almost Automorphy and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhinan Xia
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Convolution Type ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Volterra Difference Equations

We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.

scholarly journals n0-Order Weighted Pseudo Δ-Almost Automorphic Functions and Abstract Dynamic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 775 ◽  
Author(s):  
Wang ◽  
Agarwal ◽  
O’Regan ◽  
N’Guérékata
Keyword(s):  
Time Scales ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Automorphic Function ◽  
Dynamic Equations ◽  
Open Problems ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Automorphic Functions

In this paper, we introduce the concept of a n 0 -order weighted pseudo Δ n 0 δ -almost automorphic function under the matched space for time scales and we present some properties. The results are valid for q-difference dynamic equations among others. Moreover, we obtain some sufficient conditions for the existence of weighted pseudo Δ n 0 δ -almost automorphic mild solutions to a class of semilinear dynamic equations under the matched space. Finally, we end the paper with a further discussion and some open problems of this topic.

scholarly journals Bochner definition of Stepanov-like almost automorphic functions on time scales and an application to cellular neural networks with delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Li Zhang ◽  
Xu-Dong Yang
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
Dynamic Equation ◽  
Cellular Neural Networks ◽  
Automorphic Function ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Definition Of ◽  
Automorphic Functions

AbstractThe definition of Stepanov-like almost automorphic functions on time scales had been proposed in the literature, but at least one result was incorrect, which involved Bochner transform. In our work, we give the Bochner definition of Stepanov-like almost automorphic functions on time scales, and prove that a function is Stepanov-like almost automorphic if and only if it satisfies Bochner definition of Stepanov-like almost automorphic function on time scales. The Bochner definition of Stepanov-like almost automorphic functions on time scales corrects the faulty result, and perfects the definition of Stepanov-like almost automorphic functions. As applications, we discuss the almost automorphy of a certain dynamic equation and some cellular neural networks with delays on time scales.

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.

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.

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