Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term

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 and much better than those from our investigations for differential systems. The upper estimates of ε for ε-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.