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

By using operator-valued Ċ α -Fourier multiplier results on vector-valued Hölder continuous function spaces C α (ℝ; X) proved by Arendt, Batty and Bu, we obtain a necessary and sufficient condition for the C α -well-posedness for the following second order differential equations: u״ (t) = Au(t) + Bu...

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Vydáno v:	Quaestiones mathematicae Ročník 42; číslo 10; s. 1379 - 1391
Hlavní autoři:	Bu, Shangquan, Cai, Gang
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Grahamstown Taylor & Francis 26.11.2019 Taylor & Francis Ltd
Témata:	Banach spaces Continuity (mathematics) Differential equations Fourier multiplier Function space Hölder continuous function spaces Linear operators Mathematical analysis Operators (mathematics) second order differential equations Well posed problems well-posedness
ISSN:	1607-3606, 1727-933X
On-line přístup:	Získat plný text
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Popis
Shrnutí:	By using operator-valued Ċ α -Fourier multiplier results on vector-valued Hölder continuous function spaces C α (ℝ; X) proved by Arendt, Batty and Bu, we obtain a necessary and sufficient condition for the C α -well-posedness for the following second order differential equations: u״ (t) = Au(t) + Bu׳ (t) + f (t), (t ∈ ℝ), where A and B are closed linear operators on a Banach space X satisfying D(A) ⊂ D(B). We give a concrete example that our abstract result may be applied.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1607-3606 1727-933X
DOI:	10.2989/16073606.2018.1514330