# zbMATH — the first resource for mathematics

A simple almost-periodicity criterion and applications. (English) Zbl 0608.34049
A simple sufficient condition for almost periodicity of functions $$u: {\mathbb{R}}\to X$$ into a complete metric space X is observed and exploited for solutions of periodic linear ordinary differential equations in a Euclidean space (e.g. Hill’s equation) and trajectories of periodic processes on a complete metric space (e.g. semilinear partial differential equations).
Reviewer: D.Erle

##### MSC:
 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 34A30 Linear ordinary differential equations and systems
Full Text:
##### References:
 [1] Dafermos, C.M; Slemrod, M, Asymptotic behavior of nonlinear contraction semi-groups, J. funct. anal., 13, 97-106, (1973) · Zbl 0267.34062 [2] Dafermos, C.M, Almost periodic processes and almost periodic solutions of evolution equations, (), 43-57 · Zbl 0537.34045 [3] Fink, A.M, Almost periodic differential equations, () · Zbl 0325.34039 [4] Hale, J.K, Ordinary differential equations, (1969), Wiley-Interscience New York · Zbl 0186.40901 [5] Haraux, A, Asymptotic behavior of trajectories for some non autonomous almost periodic processes, J. differential equations, 49, 473-483, (1983) · Zbl 0476.34052 [6] {\scN. Kenmochi and M. Ôtani}, Asymptotic behavior of periodic systems generated by time-dependent subdifferential operators, preprint. [7] {\scN. Kenmochi and M. Ôtani}, Instability of periodic solutions of some evolution equations governed by time-dependent subdifferential operators, preprint. · Zbl 0562.34028 [8] Opial, Z, Sur une équation différentielle presque-périodique sans solution presquepériodique, Bull. acad. polon. sci., 9, 673-676, (1961) · Zbl 0100.08403
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.