Variational Methods for Almost Periodic Solutions of a Class of Neutral Delay Equations

Moez Ayachi (1) , Joël Blot (1)

1 Marin Mersenne - Pour les Mathématiques, l'Informatique et l'Interdisciplinarité

We provide new variational settings to study the a.p. (almost periodic) solutions of a class of nonlinear neutral delay equations. We extend Shu and Xu (2006) variational setting for periodic solutions of nonlinear neutral delay equation to the almost periodic settings. We obtain results on the structure of the set of the a.p. solutions, results of existence of a.p. solutions, results of existence of a.p. solutions, and also a density result for the forced equations.

Mots clés: Almost periodic solutions; Variational Methods; Neutral Delay Differential Equations

Domaines: Analyse fonctionnelle [math.FA]; Optimisation et contrôle [math.OC]

Moez Ayachi, Joël Blot. Variational Methods for Almost Periodic Solutions of a Class of Neutral Delay Equations. Abstract and Applied Analysis, 2008, Vol. 2008 (2008), Article ID 153285, 13 p. ⟨10.1155/2008/153285⟩. ⟨hal-00379264⟩