Geodesic
Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 7-29.

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Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of $\varepsilon $ for $\varepsilon $-almost-periods of solutions and their derivatives are also deduced under various restrictions imposed on the constant coefficients of the linear differential operator on the left-hand side of the given equation. Besides the existence, uniqueness and localization of almost-periodic solutions and their derivatives are established.
Classification : 34C15, 34C27, 42A75
Keywords: Almost-periodic solutions; various metrics; higher-order differential equation; nonlinear restoring term; existence and uniqueness criteria 
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Andres, Jan; Bersani, Alberto Maria; Radová, Lenka. Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 7-29. http://geodesic.mathdoc.fr/item/AUPO_2006__45_1_a0/