Alan Chavez, Samuel Castillo, Manuel Pinto
Abstract:
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.
Submitted October 10, 2013. Published February 28, 2014.
Math Subject Classifications: 47D06, 47A55, 34D05, 34G10.
Key Words: Almost automorphic functions; difference equations;
differential equation withpiecewise constant argument;
exponential dichotomy.
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Alan Chávez Universidad de Chile, Departamento de Matemáticas Facultad de Ciencias, Casilla 653 Santiago, Chile email: alancallayuc@gmail.com |
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Samuel Castillo Universidad del Bio Bio, Departamento de Matemáticas Facultad de Ciencias Concepción, Chile email: scastill@ubiobio.cl |
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Manuel Pinto Universidad de Chile, Departamento de Matemáticas Facultad de Ciencias, Casilla 653 Santiago, Chile email: pintoj@uchile.cl |
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