On a Comparison Theorem for Second Order Nonlinear Ordinary Differential Equations

Abstract

We present a comparison theorem for second order nonlinear differential equations of the form

(R (t) w (x (t)) x ’ (t)) ’ + p (t) f (x (t)) = 0 (t \in [t_{0}, β], β \leq \infty)

where $p$ is a continuous function on $[t_{0}, β)$ without any restriction on its sign.

Th. Rudek, On a Comparison Theorem for Second Order Nonlinear Ordinary Differential Equations. Z. Anal. Anwend. 14 (1995), no. 1, pp. 185–198