Well-posedness of second order degenerate differential equations in Hölder continuous function spaces

Using operator-valued Ċα-Fourier multiplier results on vector-valued Hölder continuous function spaces, we completely characterize the CαCα-well-posedness of the second order degenerate differential equations (Mu)″(t)=Au(t)+f(t)(Mu)″(t)=Au(t)+f(t) (t∈Rt∈R) and (Mu′)′(t)=Au(t)+f(t)(Mu′)′(t)=Au(t)+f(t) (t∈Rt∈R), where A,MA,M are closed operators on a Banach space XX and 0<α<10<α<1.