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Theorems of Bohr-Neugebauer-type for almost-periodic differential equations. (English) Zbl 1068.34042
The paper deals with Bohr-Neugebauer-type theorems on the almost-periodicity of every bounded solution for linear nonhomogeneous equations and systems with constant coefficients. The right-hand side is assumed to be essentially bounded and almost-periodic in various metrics (in the sense of Bohr, Stepanov, Weyl, Besicovitch). Firstly, the properties of almost-periodicity in various metrics defined for measurable functions from \(\mathbb R\) into \(\mathbb R^n\) are investigated. The almost-periodicity results in the case of almost-periodic nonhomogenities in various metrics are proved on the basis of the integral representation of entirely bounded solutions.

34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems
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