Well-posedness of Third Order Differential Equations in Holder Continuous Function Spaces

摘要

In this paper, by using operator-valued. C-alpha-Fourier multiplier results on vector-valued Holder continuous function spaces, we give a characterization of the C-alpha-well-posedness for the third order dioerential equations au"'(t) + u"(t) = Au(t) + Bu'(t) + f (t), (t is an element of R), where A, B are closed linear operators on a Banach space X such that D(A) subset of D(B), a is an element of C and 0 < alpha < 1.