Geodesic
Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 715-726

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DOI

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 $0<\unicode[STIX]{x1D6FC}<1$.
DOI : 10.4153/S0008439518000048
Mots-clés : Cα -well-posedness, degenerate differential equation, Ċα -Fourier multiplier, Hölder continuous function space 
Bu, Shangquan; Cai, Gang. Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 715-726. doi: 10.4153/S0008439518000048
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     author = {Bu, Shangquan and Cai, Gang},
     title = {Well-posedness of {Third} {Order} {Differential} {Equations} in {H\"older} {Continuous} {Function} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {715--726},
     year = {2019},
     volume = {62},
     number = {4},
     doi = {10.4153/S0008439518000048},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000048/}
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