# Generalized reciprocity for self-adjoint linear differential equations

Archivum Mathematicum (1995)

- Volume: 031, Issue: 2, page 85-96
- ISSN: 0044-8753

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topDošlý, Ondřej. "Generalized reciprocity for self-adjoint linear differential equations." Archivum Mathematicum 031.2 (1995): 85-96. <http://eudml.org/doc/247697>.

@article{Došlý1995,

abstract = {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.},

author = {Došlý, Ondřej},

journal = {Archivum Mathematicum},

keywords = {Self-adjoint equation; reciprocal equation; property BD; principal solution; minimal differential operator.Supported by the Grant No. 201/93/0452 of the Czech Grant Agency; selfadjoint equation; nonoscillatory},

language = {eng},

number = {2},

pages = {85-96},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Generalized reciprocity for self-adjoint linear differential equations},

url = {http://eudml.org/doc/247697},

volume = {031},

year = {1995},

}

TY - JOUR

AU - Došlý, Ondřej

TI - Generalized reciprocity for self-adjoint linear differential equations

JO - Archivum Mathematicum

PY - 1995

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 031

IS - 2

SP - 85

EP - 96

AB - 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.

LA - eng

KW - Self-adjoint equation; reciprocal equation; property BD; principal solution; minimal differential operator.Supported by the Grant No. 201/93/0452 of the Czech Grant Agency; selfadjoint equation; nonoscillatory

UR - http://eudml.org/doc/247697

ER -

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