Discontinuous almost automorphic functions and almost automorphic solutions of differential equations with piecewise constant arguments

• Main Authors: Alan Chavez, Samuel Castillo, Manuel Pinto
• Format: Article
• Language: English
• Published: Texas State University 2014-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: Almost automorphic functions; difference equations; differential equation withpiecewise constant argument; exponential dichotomy
• Online Access: http://ejde.math.txstate.edu/Volumes/2014/56/abstr.html

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties are used to prove the almost automorphicity of bounded solutions of a system of differential equations with piecewise constant argument. Due to the strong discrete character of these equations, the existence of a unique discrete almost automorphic solution of a non-autonomous almost automorphic difference system is obtained, for which conditions of exponential dichotomy and discrete Bi-almost automorphicity are fundamental.