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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 11, Issue 3


Almost Periodic Solutions of Monotone Second-Order Differential Equations

Moez Ayachi / Joël Blot / Philippe Cieutat
  • Université Versailles-Saint-Quentin-en-Yvelines LMV, UMR-CNRS 8100, 45 avenue des Etats-Unis, 78035 Versailles cedex, France
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Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/ans-2011-0304


We give sufficient conditions for the existence of almost periodic solutions of the secondorder 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.

Keywords: Hilbert spaces; Bohr-almost periodic; Besicovitch-almost periodic; maximal monotone operators

About the article

Published Online: 2016-03-10

Published in Print: 2011-08-01

Citation Information: Advanced Nonlinear Studies, Volume 11, Issue 3, Pages 541–554, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2011-0304.

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© 2016 by Advanced Nonlinear Studies, Inc..

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