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

Voir la notice de l'article provenant de la source Cambridge University Press

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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