Almost automorphic solutions for differential equations with piecewise constant argument

Authors

  • L.-L. Zhang Shijiazhuang Tiedao University
  • H.-X. Li Sichuan University

Keywords:

Exponential dichotomy, almost automorphic function, almost automorphic sequence, piecewise constant argument

Abstract

Using the method of exponential dichotomies, we establish a new existence and uniqueness theorem of almost automorphic solution for differential equations with piecewise constant argument of the form \(x'(t)=A(t)x(t)+B(t)x([t])+f(t), \quad t\in\mathbb{R},\)where \([\cdot]\) denotes the greatest integer function, and \(A(t), B(t):\mathbb{R}\to\mathbb{R}^{q\times q}\), \(f(t):\mathbb{R}\to\mathbb{R}^q\) are all almost automorphic. DOI: 10.1017/S0004972713001020

Author Biographies

L.-L. Zhang, Shijiazhuang Tiedao University

Department of Mathematics and Physics

H.-X. Li, Sichuan University

Department of Mathematics

Published

2014-06-03

Issue

Vol. 90 No. 1 (2014)

Section

Articles
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