A Geometrical Approach to the Second-Order Linear Differential Equation

Abstract

In this paper various concepts intrinsically defined by the differential equation 1.1 are interpreted geometrically by concepts analogous to those in the Minkowski plane. This is carried out in § 2. The point of such a development is that one may apply the techniques or transfer known results in the theory of curves (in particular, convex curves) to (1.1), thereby gaining an additional tool in the investigation of this equation. For an application of a result obtained in this way, namely (3.12), see (4). Throughout this paper, R(t) is a real-valued, continuous function of t on the real line (— ∞ < t < + ∞) and only the real solutions of (1.1) are considered.