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

摘要

In this paper, we study the half-linear differential equation with one-dimensional p-Laplacian (~(r(t)Φp)(~(x)′)) ′+c(t)~(Φp)(x)=0, where ~(Φp)(x)=| ~(x|p-2)x and p>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 p and provide new integral characterization of the principal solution.