Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments

Advances in Difference Equations

article

Feng, Zonghong¹  Wang, Yong²  Ma, Xin³ 

[1] School of Mathematics and Physics, Lanzhou Jiaotong University;School of Sciences, Southwest Petroleum University;School of Science, Southwest University of Science and Technology

关键词: Asymptotically almost periodic;    Differential equations with piecewise constant arguments;    Banach contraction fixed point theorem;    Exponential dichotomy;   

DOI  :  10.1186/s13662-020-02699-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

It is well known that differential equations with piecewise constant arguments is a class of functional differential equations, which has fascinated many scholars in recent years. These delay differential equations have been successfully applied to diverse models in real life, especially in biology, physics, economics, etc. In this work, we are interested in the existence and uniqueness of asymptotically almost periodic solution for certain differential equation with piecewise constant arguments. Due to the particularity of the equations, we cannot use the traditional method to convert it into the difference equation with exponential dichotomy. Through constructing Cauchy matrix of the investigated system to find the corresponding Green matrix of the difference equation, we need the concept of exponential dichotomy and the Banach contraction fixed point theorem of the corresponding system. Then we give some sufficient conditions to obtain the existence and uniqueness of asymptotically almost periodic solutions for these systems.

【 授权许可】

CC BY