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

In this work, we study the existence of almost periodic solutions for some partial neutral functional differential equations. Using the variation of constants formula and the spectral decomposition of the phase space developed in [M. Adimy, K. Ezzinbi, M. Laklach, Spectral decomposition for partial neutral functional differential equations, Canadian Applied Mathematics Quarterly 9 (1) (2001) 1–34], we prove that the existence of an almost periodic solution is equivalent to the existence of a bounded solution on R+R+.