A counter-example in the theory of almost periodic differential equations
type: Item
instance of: scholarly article
title: A counter-example in the theory of almost periodic differential equations
zbMATH Open document ID: 0833.34041
author: Yanyan Li
published in: Rocky Mountain Journal of Mathematics
publication date: 1995-09-17T00:00:00Z
review text: It is known that if \(a(t)\) is a piecewise continuous periodic function, then any bounded solution of \(x''+ a(t) x= 0\) is almost periodic using Floquet theory. Is it still true if \(a(t)\) is merely almost periodic? The authors show by means of a counterexample to the statement that boundedness of a solution by itself implies almost periodicity. The result is also extended to linear differential equations of order \(k\).
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 796931
zbMATH Keywords: almost periodic solutions
zbMATH Keywords: linear differential equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072293
OpenAlex ID: W1986190534
cites work: On an almost periodic Mathieu equation
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cites work: Almost periodic differential equations
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cites work: Q5798956
DOI: 10.1216/RMJM/1181072293
description: scientific article; zbMATH DE number 796931