A counter-example in the theory of almost periodic differential equations (Q1898323)
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scientific article; zbMATH DE number 796931
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counter-example in the theory of almost periodic differential equations |
scientific article; zbMATH DE number 796931 |
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A counter-example in the theory of almost periodic differential equations (English)
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17 September 1995
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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 \(k\).
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almost periodic solutions
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linear differential equations
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