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 タイトル: The Cauchy-Kovalevsky Theorem and Noncompactness Measures 著者: Ghisi, Marina 発行日: 1997年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 4 (1997), No. 3, Page 627-647 抄録: We give an abstract version of the Cauchy-Kovalevsky Theorem for the equation $u' = A(t,u)$ where $A$ is a Caratheodory operator having properties based on noncompactness measures, including Lipschitz and compactness conditions. We give an application of this result to the equation $\partial_{t}^n u + \sum_{i=1,n} f_{i}(u)B^{(n - i + 1)} \partial_{t}^{i - 1}u = 0$ that generalizes the Kirchhoff equation for the vibrating string, when $B$ is {\em not} a compact operator. Our technique is based on Nagumo's weights and on Tonelli delayed problems. URI: http://hdl.handle.net/2261/1359 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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