Well-posedness of second order differential equations in Hölder continuous function spaces - Bu, Shangquan; Cai, Gang (Quaestiones mathematicae, 2019)
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: 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) ⊂ D(B). We give a concrete example that our abstract result may be applied.