WELL-POSEDNESS OF SECOND ORDER DIFFERENTIAL EQUATIONS IN HOELDER CONTINUOUS FUNCTION SPACES

摘要

By using operator-valued C~a-Fourier multiplier results on vector-valued Hoelder continuous function spaces C~a(R;X) proved by Arendt, Batty and Bu, we obtain a necessary and sufficient condition for the C~a-well-posedness for the following second order differential equations:u''(t) = Au(t) + Bu'(t) + f{t), {t € R),where A and B are closed linear operators on a Banach space X satisfying D(A) c D(B). We give a concrete example that our abstract result may be applied.