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We give necessary and sufficient conditions for the Lp-well-posedness of the second-order degenerate differential equations with finite delay
with periodic boundary conditions (Mu)(0) = (Mu)(2π), (Mu)′(0) = (Mu)′(2π). Here A and M are closed operators on a complex Banach space X satisfying D(A) ⊂ D(M), α ∈ ℂ is fixed, F is a bounded linear operator from Lp([−2π, 0],X) into X, and ut is given by ut(s) = u(t + s) when s ∈ [−2π, 0].
