Well-posedness of degenerate differential equations in Hölder continuous function spaces

Abstract

Using known operator-valued Fourier multiplier results on vectorvalued Hölder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations {(Mu)}^{\mathit{\text{'}}}(t)=Au(t)+f(t) for t\in \mathbb{R} in Hölder continuous function spaces C^a(\mathbb{R};X)<?Pub Caret?> by the boundedness of the M-resolvent of A, where A and M are closed operators on a Banach space X satisfying D(A)\subset D(M).

Key words： Well-posedness; degenerate differential equation; {\dot{C}}^{\alpha }-multiplier; Höolder continuous function space

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