Über gewöhnliche Differentialungleichungen zweiter Ordnung

Abstract

A theorem about the separation of sub- and superfunctions υ \upsilon and w w by solutions of an ordinary differential equation of second order is proved, where υ ⩾ w \upsilon \geqslant w throughout the given interval. Examples show that the condition imposed on the right side f f of the equation is sharp, and that an analogous theorem is not true for Laplace’s equation, even in the case f ≡ 0 , υ f \equiv 0,\upsilon sub- and w w superharmonic.