Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 535-545

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

Copyright © 2005 Ondřej Došlý and Simón Peña. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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|p2x,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 p2, and the role of a minorant if p(1,2].