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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 852180, 10 pages
http://dx.doi.org/10.1155/2013/852180
Research Article

Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping

Department of Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, 10000 Zagreb, Croatia

Received 15 October 2012; Accepted 29 December 2012

Academic Editor: Yuriy Rogovchenko

Copyright © 2013 Mervan Pašić. 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

Some new oscillation criteria for a general class of second-order differential equations with nonlinear damping are shown. Except some general structural assumptions on the coefficients and nonlinear terms, we additionally assume only one sufficient condition (of Fite-Wintner-Leighton type). It is different compared to many early published papers which use rather complex sufficient conditions. Our method contains three items: classic Riccati transformations, a pointwise comparison principle, and a blow-up principle for sub- and supersolutions of a class of the generalized Riccati differential equations associated to any nonoscillatory solution of the main equation.