Periodicity, almost periodicity for time scales and related functions

• Autorzy: Chao Wang , Ravi P. Agarwal , Donal O’Regan
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

Słowa kluczowe

EN

Time scales; Almost periodic time scales; Changing periodic time scales

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 24-41

Daty

otrzymano

2015-12-09

zaakceptowano

2016-05-04

online

2016-05-30

Twórcy

autor

Chao Wang

• Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People’s Republic of China

autor

Ravi P. Agarwal

• Department of Mathematics, Texas A&M University-Kingsville, TX 78363-8202, Kingsville, TX, USA

autor

Donal O’Regan

• School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Bibliografia

• [1] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston Inc., Boston, 2001.
• [2] C.Wang, R.P. Agarwal, Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy, Adv. Differ. Equ., 296 (2015) 1-21. [WoS][Crossref]
• [3] C. Wang, Almost periodic solutions of impulsive BAM neural networks with variable delays on time scales, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014) 2828-2842. [WoS]
• [4] C. Wang, R.P. Agarwal, A classification of time scales and analysis of the general delays on time scales with applications, Math. Meth. Appl. Sci., 39 (2016) 1568-1590. [WoS]
• [5] C. Wang, R.P. Agarwal, Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive ∆- dynamic system on time scales, Appl. Math. Comput., 259 (2015) 271-292. [WoS]
• [6] C. Wang, R.P. Agarwal, A further study of almost periodic time scales with some notes and applications, Abstr. Appl. Anal., (2014) 1-11 (Article ID 267384). [WoS]
• [7] E.R. Kaufmann, Y.N. Raffoul, Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal. Appl., 319 (2006) 315-325.
• [8] Y. Li, C.Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr. Appl. Anal., (2011). 22p (Article ID 341520).
• [9] M. Adıvar, A new periodicity concept for time scales, Math. Slovaca, 63 (2013) 817-828. [WoS]
• [10] C. Wang, R.P. Agarwal, Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations, Adv. Differ. Equ., 312 (2015) 1-9. [Crossref]
• [11] A. Wilansky, Topics in Functional Analysis, Springer, Lecture Notes in Mathematics, Volume 45 (1967).
• [12] Y. Li, B. Li, Almost periodic time scales and almost periodic functions on time scales, J. Appl. Math., (2015) 1-8 (Article ID 730672).
• [13] B. Sendov, Hausdorff Approximations, Kluwer Academic Publishers, Netherlands, (1990).

Identyfikatory

DOI

10.1515/msds-2016-0003