A COUNTER-EXAMPLE IN THE THEORY OF ALMOST PERIODIC DIFFERENTIAL EQUATIONS

We show by means of an explicit example that a bounded solution of the real two-term differential equation of the second order, x″ + a(t)x = 0, t ϵ R, where a(t) is Bohr almost periodic, is not almost periodic. This disproves various claims which have appeared in the literature. We also provide such...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 1995, Vol.25 (1), p.437-440
Hauptverfasser: MINGARELLI, A.B., PU, F.Q., ZHENG, L.
Format: Artikel
Sprache:eng
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Zusammenfassung:We show by means of an explicit example that a bounded solution of the real two-term differential equation of the second order, x″ + a(t)x = 0, t ϵ R, where a(t) is Bohr almost periodic, is not almost periodic. This disproves various claims which have appeared in the literature. We also provide such an example for the general linear equation of order k, ≥ 2, with almost periodic coefficients.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmjm/1181072293