Sufficient conditions for the $n$-th order linear differential equation are derived which guarantee that its Cauchy function $K$, together with its derivatives ${\partial ^i K}\over {\partial t^i}$, $i=1,\dots ,n-1$, is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.
@article{107606,
author = {Valter \v Seda},
title = {Some classes of linear $n$th-order differential equations},
journal = {Archivum Mathematicum},
volume = {033},
year = {1997},
pages = {157-165},
zbl = {0914.34011},
mrnumber = {1464310},
language = {en},
url = {http://dml.mathdoc.fr/item/107606}
}
Šeda, Valter. Some classes of linear $n$th-order differential equations. Archivum Mathematicum, Tome 033 (1997) pp. 157-165. http://gdmltest.u-ga.fr/item/107606/
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