Geodesic
Some classes of linear $n$th-order differential equations
Archivum mathematicum, Tome 33 (1997) no. 1-2, pp. 157-165
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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.
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.
Classification : 34A40, 34D05
Keywords: Cauchy function; Čaplygin comparison theorem; monotonic solutions; regularity of bands 
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Šeda, Valter. Some classes of linear $n$th-order differential equations. Archivum mathematicum, Tome 33 (1997) no. 1-2, pp. 157-165. http://geodesic.mathdoc.fr/item/ARM_1997_33_1-2_a16/

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