SPECTRAL DECOMPOSITION FOR PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

MOSTAFA ADIMY, KHALIL EZZINBI AND MOSTAFA LAKLACH

Abstract. A class of partial neutral functional differential equations with a non dense domain is considered. In the first part the spectral decomposition of a state space into stable, unstable and center subspaces is obtained. In the second part a variation-of-constants formula for the perturbed linear equation is given. In the third part, the existence of bounded solutions is investigated. As a consequence in the hyperbolic case, the existence of periodic (or almost periodic) solutions is established. This work extends our previous results on partial functional differential equations with non dense domain [4] and re sults in [54].