On Constants in Nonoscillation Criteria for Half-Linear Differential Equations

Abstract

We study the half-linear differential equation (r(t)Φ(x′))′+c(t)Φ(x)=0, where Φ(x)=|x|p−2x, p>1. Using the modified Riccati technique, we derive new nonoscillation criteria for this equation. The results are closely related to the classical Hille-Nehari criteria and allow to replace the fixed constants in known nonoscillation criteria by a certain one-parametric expression.