Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces
Keyword(s):
AbstractIn 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 $0<\unicode[STIX]{x1D6FC}<1$.
2014 ◽
Vol 10
(2)
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pp. 239-248
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2016 ◽
Vol 34
(2)
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pp. 223-236
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2011 ◽
Vol 71
(2)
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pp. 259-274
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2017 ◽
Vol 219
(2)
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pp. 727-755
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2017 ◽
Vol 288
(1)
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pp. 27-46
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