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ON EXPONENTIALLY BOUNDED $¥alpha$ -TIMES INTEGRATED C-COSINE FUNCTIONS
http://hdl.handle.net/10131/5765
http://hdl.handle.net/10131/576593beb5aa-fc3f-4ce6-b957-c99153d09dec
名前 / ファイル | ライセンス | アクション |
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YMJ_52_N1_2005_059-072.pdf (1.0 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-12-15 | |||||
タイトル | ||||||
タイトル | ON EXPONENTIALLY BOUNDED $¥alpha$ -TIMES INTEGRATED C-COSINE FUNCTIONS | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Kuo, Chubg-Cheng
× Kuo, Chubg-Cheng |
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著者所属 | ||||||
Department of Mathematics, Fu Jen University,Taipei, Taiwan 24205, R.O.C. | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | In this paper we apply some basic properties concerning $¥alpha$-times integrated C-cosine functions to deduce a characterization of an exponentially bounded $¥alpha$-times integrated C-cosine function in terms of its Laplace transform, and then use it to show that for each $x¥in(¥lambda^{2}-A)^{-1}CX$ the second order abstract Cauchy problem: $t^{¥alpha-1}$ $u^{¥prime¥prime}(t)=Au(t)+_{¥overline{¥Gamma(¥alpha)}}x$ for $t>0,u(O)=u^{¥prime}(0)=0$ has a unique solution $u(¥cdot)$ which satisfies $||u(t)¥Vert,||u^{¥prime¥prime}(t)||¥in O(e^{¥omega t})$ as $ t¥rightarrow¥infty$ when the closed linear operator $A$ : $D(A)¥subset X¥rightarrow X$ which generates an exponentially bounded $¥alpha$-times integrated C-cosine function $C(¥cdot)$ on a Banach space $X$ with $||C(t)||¥leq Me^{¥{vt}$ for all $t¥geq 0$ and for some fixed $M¥omega¥geq 0.Moreover$ , we show that a closed linear operator in $X$ generates an exponentially bounded $¥alpha$-times integrated C-cosine function on $X$ also generates an exponentially bounded $¥underline{¥alpha}$times integrated C-semigroup on X. | |||||
書誌情報 |
Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学 巻 52, 号 1, p. 59-72, 発行日 2005 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00440523 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0089285X | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
出版者 | ||||||
出版者 | Yokohama City University and Yokohama National University |