Title:
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Generalized reciprocity for self-adjoint linear differential equations (English) |
Author:
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Došlý, Ondřej |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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31 |
Issue:
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2 |
Year:
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1995 |
Pages:
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85-96 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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Let $L(y)=y^{(n)}+q_{n-1}(t)y^{(n-1)}+\dots +q_0(t)y,\,t\in [a,b)$, be an $n$-th order differential operator, $L^*$ be its adjoint and $p,w$ be positive functions. It is proved that the self-adjoint equation $L^*\bigl (p(t)L(y)\bigr ) =w(t)y$ is nonoscillatory at $b$ if and only if the equation $L\bigl (w^{-1}(t)L^*(y)\bigr )=p^{-1}(t)y$ is nonoscillatory at $b$. Using this result a new necessary condition for property BD of the self-adjoint differential operators with middle terms is obtained. (English) |
Keyword:
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Self-adjoint equation |
Keyword:
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reciprocal equation |
Keyword:
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property BD |
Keyword:
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principal solution |
Keyword:
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minimal differential operator.Supported by the Grant No. 201/93/0452 of the Czech Grant Agency |
MSC:
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34B05 |
MSC:
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34C10 |
MSC:
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34L05 |
idZBL:
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Zbl 0841.34032 |
idMR:
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MR1357977 |
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Date available:
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2008-06-06T21:28:16Z |
Last updated:
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2012-05-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/107529 |
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Reference:
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