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On almost periodic solution of differential equations with piecewise constant argument

Published online by Cambridge University Press:  03 July 2006

RONG YUAN
RONG YUAN
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, P.R. China. e-mail: ryuan@bnu.edu.cn
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Abstract

We study the spectrum containment of almost periodic solutions to differential equations with piecewise constant argument (EPCA, for short). We find an important property, which is different from that given by Cartwright for Ordinary Differential Equations (ODE). Some known (periodic, quasi-periodic) results may be expanded. As a corollary, it is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. As a consequence, a new class of quasi-periodic functions is described. This new phenomenon is due to the piecewise constant argument and illustrates a crucial difference between ODE and EPCA.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 1 , July 2006 , pp. 161 - 174
Copyright
2006 Cambridge Philosophical Society

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