The Distribution of Zeroes and Critical Points of Solutions of a Second Order Half-Linear Differential Equation

This paper reuses an idea first devised by Kwong to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second order half-linear differential equation(p(x)Φ(y'))'+q(x)Φ(y)=0, withp(x),q(x)>0,Φ(t)=|t|r-2t, andrreal such thatr>1. It also compares it with other methods developed by the authors.