Note on a non-oscillation theorem of Atkinson

We present a general non-oscillation criterion for a second order two-term scalar nonlinear differential equation in the spirit of a classic result by Atkinson [1]. The presentation is simpler than most and can serve to unify many such criteria under one common theme that eliminates the need for specfic techniques in each of the classical cases (sublinear, linear, and superlinear). As is to be expected in a result of this kind, the applications are widespread and include, but are not limited to, linear, sublinear, superlinear differential equations as well as some transcendental cases and some possibly mixed cases.