Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales

Yongkun Li; Pan Wang

doi:10.3934/dcdss.2017022

Article Contents

2017, Volume 10, Issue 3: 463-473. Doi: 10.3934/dcdss.2017022

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Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales

Yongkun Li^, and
Pan Wang

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

^* Corresponding author: Yongkun Li
^* Corresponding author: Yongkun Li

Received: October 31, 2015

Revised: November 30, 2016

Published: May 2017

The first author is supported by the National Natural Sciences Foundation of China under Grant 11361072.

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Abstract

We first propose a concept of almost periodic functions in the sense of Stepanov on time scales. Then, we consider a class of neutral functional dynamic equations with Stepanov-almost periodic terms on time scales in a Banach space. By means of the contraction mapping principle, we establish some criteria for the existence and uniqueness of almost periodic solutions for this class of dynamic equations on time scales. Finally, we give an example to illustrate the effectiveness of our results.

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Mathematics Subject Classification: Primary: 34K40, 34K14; Secondary: 34N05.

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