Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 5, Pages 535-545
doi:10.1155/JIA.2005.535

A linearization method in oscillation theory of half-linear second-order differential equations

Ondřej Došlý and Simón Peña

 Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, Brno CZ-662 95, Czech Republic
Received 22 December 2003

Abstract

Using inequalities for a certain function appearing in the half-linear version of Picone's identity, we show that oscillatory properties of the half-linear second-order differential equation (r(t)Φ(x′))′+c(t)Φ(x)=0, Φ(x)=|x|p−2x,p>1, can be investigated via oscillatory properties of a certain associated second-order linear differential equation. This linear equation plays the role of a Sturmian majorant, in a certain sense, if p≥2, and the role of a minorant if p∈(1,2].