Bohr-Neugebauer type theorem for some partial neutral functional differential equations

Mostafa Adimy (1, 2) , Abdelhai Elazzouzi (3) , Khalil Ezzinbi (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics
3 Département de mathématiques [FSSM]

In this work, we study the existence of almost periodic solutions for some partial neutral functional differential equations. Using the variation of constants formulaand the spectral decomposition of the phase space developed in [6], we prove that the existence of an almost periodic solution is equivalent to the existence of a bounded solution on $\mathbb{R}^+$.

Mots clés: neutral equation; Hille-Yosida condition; semigroup; variation of constants formula; essential growth; spectral decomposition; almost periodic solution

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Théorie spectrale [math.SP]

Mostafa Adimy, Abdelhai Elazzouzi, Khalil Ezzinbi. Bohr-Neugebauer type theorem for some partial neutral functional differential equations. 2006. ⟨hal-00258398⟩