科研之友
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摘要
By using operator-valued (C) over dot(alpha)-Fourier multiplier results on vector-valued Holder continuous function spaces C-alpha(R; X) proved by Arendt, Batty and Bu, we obtain a necessary and sufficient condition for the C-alpha-well-posedness for the following second order differential equations: @@@ u ''(t) = Au(t) + Bu'(t) + f (t), (t is an element of R), @@@ where A and B are closed linear operators on a Banach space X satisfying D(A) subset of D(B). We give a concrete example that our abstract result may be applied.
