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
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.
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].