Periodic solutions for a Cauchy problem on time scales

This paper firstly shows that there does not exist a nonzero periodic solution for a nonhomogeneous Cauchy problem by using the Laplace transformation on time scales. Secondly, two new Gronwall inequalities, which play an important role in the qualitative analysis of differential and integral equati...

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Main Author:	Fode Zhang
Format:	Article
Language:	English
Published:	Emerald Publishing 2015-07-01
Series:	Arab Journal of Mathematical Sciences
Subjects:	Asymptotically periodic solutions Cauchy problem Time scales Gronwall inequality
Online Access:	http://www.sciencedirect.com/science/article/pii/S1319516615000134

id	doaj-65c99bfdd1d54f13919ced0eb7d89f38
record_format	Article
spelling	doaj-65c99bfdd1d54f13919ced0eb7d89f382021-05-02T18:45:33ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662015-07-0121223725210.1016/j.ajmsc.2015.04.002Periodic solutions for a Cauchy problem on time scalesFode ZhangThis paper firstly shows that there does not exist a nonzero periodic solution for a nonhomogeneous Cauchy problem by using the Laplace transformation on time scales. Secondly, two new Gronwall inequalities, which play an important role in the qualitative analysis of differential and integral equations, are established. Thirdly, by employing the contraction mapping principle, existence and uniqueness results of weighted S-asymptotically ω-periodic solutions for nonlinear Cauchy problem on time scales are obtained in an asymptotically periodic function space. Finally, some examples are presented to illustrate some of the results described here.http://www.sciencedirect.com/science/article/pii/S1319516615000134Asymptotically periodic solutionsCauchy problemTime scalesGronwall inequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Fode Zhang
spellingShingle	Fode Zhang Periodic solutions for a Cauchy problem on time scales Arab Journal of Mathematical Sciences Asymptotically periodic solutions Cauchy problem Time scales Gronwall inequality
author_facet	Fode Zhang
author_sort	Fode Zhang
title	Periodic solutions for a Cauchy problem on time scales
title_short	Periodic solutions for a Cauchy problem on time scales
title_full	Periodic solutions for a Cauchy problem on time scales
title_fullStr	Periodic solutions for a Cauchy problem on time scales
title_full_unstemmed	Periodic solutions for a Cauchy problem on time scales
title_sort	periodic solutions for a cauchy problem on time scales
publisher	Emerald Publishing
series	Arab Journal of Mathematical Sciences
issn	1319-5166
publishDate	2015-07-01
description	This paper firstly shows that there does not exist a nonzero periodic solution for a nonhomogeneous Cauchy problem by using the Laplace transformation on time scales. Secondly, two new Gronwall inequalities, which play an important role in the qualitative analysis of differential and integral equations, are established. Thirdly, by employing the contraction mapping principle, existence and uniqueness results of weighted S-asymptotically ω-periodic solutions for nonlinear Cauchy problem on time scales are obtained in an asymptotically periodic function space. Finally, some examples are presented to illustrate some of the results described here.
topic	Asymptotically periodic solutions Cauchy problem Time scales Gronwall inequality
url	http://www.sciencedirect.com/science/article/pii/S1319516615000134
work_keys_str_mv	AT fodezhang periodicsolutionsforacauchyproblemontimescales
_version_	1721488756305821696

Periodic solutions for a Cauchy problem on time scales

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