Trivial differential equations in spaces $L_p, 0 < p< 1$
A description of the set $X_p$ &nbsp;of all solutions of the trivial Cauchy problem in $L_p, 0 &lt; p&lt; 1$ is presented. The principal result is Theorem 2, which asserts that $X_p$ is a closed subspace of the $p$ -Banach space $H_p$ of all curves in $L_p$ that satisfy a Höl...
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| Datum: | 1992 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8176 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | A description of the set $X_p$ &nbsp;of all solutions of the trivial Cauchy problem in $L_p, 0 &lt; p&lt; 1$ is presented. The principal result is Theorem 2, which asserts that $X_p$ is a closed subspace of the $p$ -Banach space $H_p$ of all curves in $L_p$ that satisfy a Hölder condition of order $р$ &nbsp;and emanate from relative to the $p$ -norm, which is equal to the minimal constant in the Hölder condition. |
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