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hal-00560960, version 1

Almost periodic solutions of monotone second-order differential equations

Moez Ayachi () 1, Joël Blot 1, Philippe Cieutat (Author to contact preferably) 2

advanced nonlinear studies 11, 3 (2011) 541-554

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.

  • 1:  Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)
  • Université Paris I - Panthéon-Sorbonne
  • 2:  Laboratoire de Mathématiques de Versailles (LM-Versailles)
  • CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines
  • Domain : Mathematics/Functional Analysis
    Mathematics/Dynamical Systems
    Mathematics/Classical Analysis and ODEs
 
  • hal-00560960, version 1
  • http://hal-paris1.archives-ouvertes.fr/hal-00560960
  • oai:hal-paris1.archives-ouvertes.fr:hal-00560960
  • From: Moez Ayachi <>
  • Submitted on: Monday, 31 January 2011 13:17:19
  • Updated on: Monday, 5 March 2012 16:26:49