Well-posedness of second order degenerate differential equations in Hölder continuous function spaces - Bu, Shangquan; Cai, Gang (Expositiones mathematicae, 2016)
Using operator-valued Ċα-Fourier multiplier results on vector-valued Hölder continuous function spaces, we completely characterize the Cα-well-posedness of the second order degenerate differential equations (Mu)″(t)=Au(t)+f(t) (t∈R) and (Mu′)′(t)=Au(t)+f(t) (t∈R), where A,M are closed operators on a Banach space X and 0<α<1.