On the existence of almost periodic solutions for a class of neutral delay differential equations

Moez Ayachi (1) , Dhaou Lassoued (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

We study the existence of a Besicovitch almost periodic solution for a class of second order neutral delay differential equations u''(t−r)+D_1F(u(t−r),u(t−2r),t−r)+D_2F(u(t),u(t−r),t) = 0, in a Hilbert space, under some hyptoheses on the function F(*,*,t). Here, F : H×H×R → R denotes a differentiable function, D_j, j = 1,2, denotes the partial differential with respect to the jth vector variable and r ∈ (0,∞) is a fixed real number. The approach we use is based on a variational method applied on a Hilbert space of Besicovitch almost periodic functions

Mots clés: Besicovitch almost periodic solutions; neutral delay differential equations; variational methods

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Moez Ayachi, Dhaou Lassoued. On the existence of almost periodic solutions for a class of neutral delay differential equations. Facta Universitatis. Series Mathematics and Informatics, 2014, 29 (2), pp.1-14. ⟨hal-00999774⟩