Half-linear ODE and modified Riccati equation: Comparison theorems, integral characterization of principal solution

In this paper, we study the half-linear differential equation with one-dimensional pp-Laplacian (r(t)Φp(x′))′+c(t)Φp(x)=0,(r(t)Φp(x′))′+c(t)Φp(x)=0, where Φp(x)=|x|p−2xΦp(x)=|x|p−2x and p>1p>1. Using a suitable modification of the so-called linearization technique, we derive new results which allow to compare the solutions of two equations with different pp and provide new integral characterization of the principal solution.