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

Using operator-valued Ċα-Fourier multiplier results on vector-valued Hölder continuous function spaces, we completely characterize the Cα-well-posedness of the second order degenerate differential equations (Mu)″(t)=Au(t)+f(t) (t∈R) and (Mu′)′(t)=Au(t)+f(t) (t∈R), where A,M are closed operators on...

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Vydané v:	Expositiones mathematicae Ročník 34; číslo 2; s. 223 - 236
Hlavní autori:	Bu, Shangquan, Cai, Gang
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier GmbH 2016
Predmet:	[formula omitted]-Fourier multiplier [formula omitted]-well-posedness Degenerate differential equations Hölder continuous function spaces secondary Ċα-Fourier multiplier Cα-well-posedness Degenerate differential equations Hölder continuous function spaces primary
ISSN:	0723-0869, 1878-0792
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Shrnutí:	Using operator-valued Ċα-Fourier multiplier results on vector-valued Hölder continuous function spaces, we completely characterize the Cα-well-posedness of the second order degenerate differential equations (Mu)″(t)=Au(t)+f(t) (t∈R) and (Mu′)′(t)=Au(t)+f(t) (t∈R), where A,M are closed operators on a Banach space X and 0<α<1.
ISSN:	0723-0869 1878-0792
DOI:	10.1016/j.exmath.2015.07.003