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Abstract and Applied Analysis
Volume 2014, Article ID 258159, 14 pages
http://dx.doi.org/10.1155/2014/258159
Research Article

Conditional Oscillation of Half-Linear Differential Equations with Coefficients Having Mean Values

1Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
2Department of Mathematics, Faculty of Forestry and Wood Technology, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic

Received 3 February 2014; Accepted 12 June 2014; Published 8 July 2014

Academic Editor: Yuriy Rogovchenko

Copyright © 2014 Petr Hasil et al. 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

We prove that the existence of the mean values of coefficients is sufficient for second-order half-linear Euler-type differential equations to be conditionally oscillatory. We explicitly find an oscillation constant even for the considered equations whose coefficients can change sign. Our results cover known results concerning periodic and almost periodic positive coefficients and extend them to larger classes of equations. We give examples and corollaries which illustrate cases that our results solve. We also mention an application of the presented results in the theory of partial differential equations.