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Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 4 / December 2019
- Published online by Cambridge University Press:
- 15 October 2018, pp. 715-726
- Print publication:
- December 2019
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- Article
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In this paper, by using operator-valued
${\dot{C}}^{\unicode[STIX]{x1D6FC}}$-Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the 
$C^{\unicode[STIX]{x1D6FC}}$-well-posedness for the third order differential equations 
$au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$, (
$t\in \mathbb{R}$), where 
$A,B$ are closed linear operators on a Banach space 
$X$ such that 
$D(A)\subset D(B)$, 
$a\in \mathbb{C}$ and 
$0<\unicode[STIX]{x1D6FC}<1$.
