Almost periodic solutions of monotone second-order differential equations

Abstract : We give sufficient conditions for the existence of almost periodic solutions of the following second-order differential equation: u′′(t) = f(u(t)) + e(t) on a Hilbert space H, where the vector field f : H −→ H is monotone, continuous and the forcing term e : R −→ H is almost periodic. Notably, we state a result of existence and uniqueness of the Besicovitch almost periodic solution, then we approximate this solution by a sequence of Bohr almost periodic solutions.
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https://hal-paris1.archives-ouvertes.fr/hal-00560960
Contributor : Moez Ayachi <>
Submitted on : Monday, January 31, 2011 - 1:17:19 PM
Last modification on : Thursday, February 7, 2019 - 4:00:58 PM

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  • HAL Id : hal-00560960, version 1

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Moez Ayachi, Joël Blot, Philippe Cieutat. Almost periodic solutions of monotone second-order differential equations. advanced nonlinear studies, 2011, 11 (3), pp.541-554. ⟨hal-00560960⟩

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