Almost periodic solutions of monotone second-order differential equations

Moez Ayachi (1) , Joël Blot (1) , Philippe Cieutat (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LMV - Laboratoire de Mathématiques de Versailles

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.

Domains: Functional Analysis [math.FA]; Dynamical Systems [math.DS]; Classical Analysis and ODEs [math.CA]

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⟩