LAUSR

In this paper, we characterize the $$C^\alpha $$Cα-well-posedness of the second order degenerate differential equation with finite delay $$(Mu)''(t) = Au(t) + Fu_t + f(t)$$(Mu)′′(t)=Au(t)+Fut+f(t), ($$t\in {\mathbb R}$$t∈R) by using known operator-valued Fourier multiplier results on $$C^\alpha ({\mathbb R}; X)$$Cα(R;X), where A, M are closed linear operators on a complex Banach space X satisfying $$D(A)\cap D(M) \not =\{0\}$$D(A)∩D(M)≠{0}, $$r > 0$$r>0 is fixed and F is a bounded linear operator from $$C([-r, 0]; X)$$C([-r,0];X) into X.