Open Access

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

Journal of Inequalities and Applications20052005:658372

DOI: 10.1155/JIA.2005.535

Received: 22 December 2003

Published: 31 October 2005

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 https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.535/MediaObjects/13660_2003_Article_1542_IEq1_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.535/MediaObjects/13660_2003_Article_1542_IEq2_HTML.gif , 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 https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.535/MediaObjects/13660_2003_Article_1542_IEq3_HTML.gif , and the role of a minorant if https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.535/MediaObjects/13660_2003_Article_1542_IEq4_HTML.gif .

Authors’ Affiliations

(1)
Department of Mathematics, Masaryk University

Copyright

© Došlý and Peña 2005