Geodesic
Eventual disconjugacy of $y^{(n)} + \mu p(x) y = 0$ for every $\mu $
Archivum mathematicum, Tome 40 (2004) no. 2, pp. 193-200 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34C10
Keywords: eventual disconjugacy 
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     title = {Eventual disconjugacy of $y^{(n)} + \mu p(x) y = 0$ for every $\mu $},
     journal = {Archivum mathematicum},
     pages = {193--200},
     year = {2004},
     volume = {40},
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     zbl = {1116.34317},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2004_40_2_a5/}
}
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Elias, Uri. Eventual disconjugacy of $y^{(n)} + \mu p(x) y = 0$ for every $\mu $. Archivum mathematicum, Tome 40 (2004) no. 2, pp. 193-200. http://geodesic.mathdoc.fr/item/ARM_2004_40_2_a5/

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