scholarly journals The dynamic analysis on a class of stochastic impulsive equations with doubly weighted pseudo almost automorphic coefficients on time scales

2021 ◽  
Author(s):  
Ping Zhu
Keyword(s):  
Dynamic Analysis ◽  
Stochastic Processes ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Translation Invariance ◽  
New Approach ◽  
Impulsive Equations ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

Devoting to exploring the translation invariance and convolution invariance of doubly weighted pseudo almost automorphic stochastic processes with impulses on time scales proposed in this paper. Based on these results, taking advantage of a new approach to obtain the existence and uniqueness of the doubly weighted pseudo almost automorphic solutions to a class of stochastic nonlinear impulsive equations on time scales, which enrich the dynamics of doubly weighted pseudo almost automorphic stochastic processes. Finally, an example is researched to illustrate our conclusions.

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.

scholarly journals Almost Automorphic Functions of Ordernand Applications to Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Gisèle Mophou ◽  
Gaston Mandata N’Guérékata ◽  
Aril Milce
Keyword(s):  
Time Scales ◽  
Existence And Uniqueness ◽  
Dynamical Equation ◽  
Time Varying ◽  
First Order ◽  
Time Varying Delay ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Varying Delay ◽  
Automorphic Functions

We revisit the notion on almost automorphic functions on time scales given by Lizama and Mesquita (2013). Then we present the notion of almost automorphic functions of ordern. Finally, we apply this notion to study the existence and uniqueness and the global stability of almost automorphic solution of first order to a dynamical equation with finite time varying delay.

scholarly journals Existence and Uniqueness of Pseudo Almost Automorphic Mild Solutions to Some Classes of Partial Hyperbolic Evolution Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Evolution Equation ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Existence And Uniqueness Theorem ◽  
Abstract Result ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

We will establish an existence and uniqueness theorem of pseudo almost automorphic mild solutions to the following partial hyperbolic evolution equation(d/dt)[u(t)+f(t,Bu(t))]=Au(t)+g(t,Cu(t)),  t∈ℝ,under some assumptions. To illustrate our abstract result, a concrete example is given.

scholarly journals (Weighted pseudo) almost automorphic solutions in distribution for fractional stochastic differential equations driven by levy noise

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2403-2424
Author(s):  
Min Yang
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Analysis ◽  
Contraction Principle ◽  
Lévy Noise ◽  
Almost Automorphic ◽  
Fractional Stochastic Differential Equations ◽  
Pseudo Almost Automorphic

In this paper, by using contraction principle, fractional calculus and stochastic analysis, we study the existence and uniqueness of (weighted pseudo) almost automorphic solutions in distribution for fractional stochastic differential equations driven by L?vy noise. An example is presented to illustrate the application of the abstract results.

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.

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