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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Veröffentlicht in:Expositiones mathematicae Jg. 34; H. 2; S. 223 - 236
Hauptverfasser: Bu, Shangquan, Cai, Gang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier GmbH 2016
Schlagworte:
[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
Online-Zugang:Volltext
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Zusammenfassung: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