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Cauchy function; Čaplygin comparison theorem; monotonic solutions; regularity of bands
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.
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