scholarly journals Stepanov-like pseudo almost periodic functions on time scales and applications to dynamic equations with delay

2018 ◽  
Vol 16 (1) ◽  
pp. 826-841 ◽  
Author(s):  
Chao-Hong Tang ◽  
Hong-Xu Li
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Translation Invariance ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic ◽  
Equations With Delay

AbstractIn this paper, we introduce the concept of Sp-pseudo almost periodicity on time scales and present some basic properties of it, including the translation invariance, uniqueness of decomposition, completeness and composition theorem. Moreover, we prove the seemingly simple but nontrivial result that pseudo almost periodicity implies Stepanov-like pseudo almost periodicity. As an application of the abstract results, we present some existence and uniqueness results on the pseudo almost periodic solutions of dynamic equations with delay.

scholarly journals (ω, c)- Pseudo almost periodic distributions

2020 ◽  
Vol 7 (1) ◽  
pp. 237-248 ◽  
Author(s):  
Mohammed Taha Khalladi ◽  
Abdelkader Rahmani
Keyword(s):  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Differential Systems ◽  
Schwartz Distributions ◽  
Pseudo Almost Periodic Solutions ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic

AbstractThe paper is a study of the (w, c) −pseudo almost periodicity in the setting of Sobolev-Schwartz distributions. We introduce the space of (w, c) −pseudo almost periodic distributions and give their principal properties. Some results about the existence of distributional (w, c) −pseudo almost periodic solutions of linear differential systems are proposed.

scholarly journals Bochner-Like Transform and Stepanov Almost Periodicity on Time Scales with Applications

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 566 ◽  
Author(s):  
Chao-Hong Tang ◽  
Hong-Xu Li
Keyword(s):  
Time Scales ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Basic Properties ◽  
Composition Theorem

By using Bochner transform, Stepanov almost periodic functions inherit some basic properties directly from almost periodic functions. Recently, this old work was extended to time scales. However, we show that Bochner transform is not valid on time scales. Then we present a revised version, called Bochner-like transform, for time scales, and prove that a function is Stepanov almost periodic if and only if its Bochner-like transform is almost periodic on time scales. Some basic properties including the composition theorem of Stepanov almost periodic functions are obtained by applying Bochner-like transform. Our results correct the recent results where Bochner transform is used on time scales. As an application, we give some results on dynamic equations with Stepanov almost periodic terms.

scholarly journals A Further Study of Almost Periodic Time Scales with Some Notes and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
Dynamic Equations ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Cauchy Matrix ◽  
Nonlinear Dynamic Equations ◽  
Almost Periodic Time Scales

We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in Li and Wang (2011) and several examples of almost periodic time scales which are not periodic are provided. Furthermore, the concepts of almost periodic functions are redefined under the sense of this new timescale concept. Finally, almost periodicity of Cauchy matrix for dynamic equations is proved under these new definitions. Based on these results, the existence of almost periodic solutions to a class of nonlinear dynamic equations is investigated by the almost periodicity of Cauchy matrix on almost periodic time scales. Besides, as an application, we apply our results to a class of high-order Hopfield neural networks.

DYNAMICS OF PSEUDO ALMOST PERIODIC SOLUTION FOR IMPULSIVE NEOCLASSICAL GROWTH MODEL

2017 ◽  
Vol 58 (3-4) ◽  
pp. 359-367 ◽  
Author(s):  
ZHINAN XIA
Keyword(s):  
Periodic Solution ◽  
Growth Model ◽  
Almost Periodic Solution ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solution ◽  
Neoclassical Growth Model ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic ◽  
Neoclassical Growth

This paper analyses the pseudo almost periodicity of the impulsive neoclassical growth model. We investigate the existence, uniqueness and exponential stability of the pseudo almost periodic solution. Moreover, an example is given to illustrate the significance of the main findings.

scholarly journals Time Remotely Almost Periodic Viscosity Solutions of Hamilton-Jacobi Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Shilin Zhang ◽  
Daxiong Piao
Keyword(s):  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Almost Periodic Functions ◽  
Periodic Case ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Jacobi Equations

We study some properties of the remotely almost periodic functions. This paper studies viscosity solutions of general Hamilton-Jacobi equations in the time remotely almost periodic case. Existence and uniqueness results are presented under usual hypotheses.

scholarly journals Almost Periodic Solutions for Second Order Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Lan Li
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions

We firstly introduce the concept and the properties ofCmalmost periodic functions on time scales, which generalizes the concept of almost periodic functions on time scales and the concept ofC(n)-almost periodic functions. Secondly, we consider the existence and uniqueness of almost periodic solutions for second order dynamic equations on time scales by Schauder’s fixed point theorem and contracting mapping principle. At last, we obtain alternative theorems for second order dynamic equations on time scales.

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