Eventual disconjugacy of $y^{\left(n\right)}+\mu p\left(x\right)y=0$ for every $\mu$

Elias, Uri. "Eventual disconjugacy of $y^{(n)} + \mu p(x) y = 0$ for every $\mu $." Archivum Mathematicum 040.2 (2004): 193-200. <http://eudml.org/doc/249298>.

@article{Elias2004,
abstract = {The work characterizes when is the equation $ y^\{ (n) \} + \mu p(x) y = 0 $ eventually disconjugate for every value of $ \mu $ and gives an explicit necessary and sufficient integral criterion for it. For suitable integers $ q $, the eventually disconjugate (and disfocal) equation has 2-dimensional subspaces of solutions $ y $ such that $ y^\{ (i) \} > 0 $, $ i = 0, \ldots , q-1 $, $ (-1)^\{i-q\} y^\{ (i) \} > 0 $, $ i = q, \ldots , n $. We characterize the “smallest” of such solutions and conjecture the shape of the “largest” one. Examples demonstrate that the estimates are sharp.},
author = {Elias, Uri},
journal = {Archivum Mathematicum},
keywords = {eventual disconjugacy},
language = {eng},
number = {2},
pages = {193-200},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Eventual disconjugacy of $y^\{(n)\} + \mu p(x) y = 0$ for every $\mu $},
url = {http://eudml.org/doc/249298},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Elias, Uri
TI - Eventual disconjugacy of $y^{(n)} + \mu p(x) y = 0$ for every $\mu $
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 2
SP - 193
EP - 200
AB - The work characterizes when is the equation $ y^{ (n) } + \mu p(x) y = 0 $ eventually disconjugate for every value of $ \mu $ and gives an explicit necessary and sufficient integral criterion for it. For suitable integers $ q $, the eventually disconjugate (and disfocal) equation has 2-dimensional subspaces of solutions $ y $ such that $ y^{ (i) } > 0 $, $ i = 0, \ldots , q-1 $, $ (-1)^{i-q} y^{ (i) } > 0 $, $ i = q, \ldots , n $. We characterize the “smallest” of such solutions and conjecture the shape of the “largest” one. Examples demonstrate that the estimates are sharp.
LA - eng
KW - eventual disconjugacy
UR - http://eudml.org/doc/249298
ER -