Research Article

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

Published in: Quaestiones Mathematicae
Volume 42 , issue 10 , 2019 , pages: 1379–1391

DOI: 10.2989/16073606.2018.1514330

Author(s): Shangquan Bu , China , Gang Cai , China

Keywords: 34G10 , 47D06 , 47A10 , 34K30 , 34G10 , 47D06 , 47A10 , 34K30

Abstract

By using operator-valued Ċ^α -Fourier multiplier results on vector-valued Hölder continuous function spaces C^α (ℝ; X) proved by Arendt, Batty and Bu, we obtain a necessary and sufficient condition for the C^α -well-posedness for the following second order differential equations:

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