Abstract and Applied Analysis
Volume 2011 (2011), Article ID 638271, 15 pages
http://dx.doi.org/10.1155/2011/638271
Research Article

On Constants in Nonoscillation Criteria for Half-Linear Differential Equations

Simona Fišnarová and Robert Mařík

Department of Mathematics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic

Received 15 June 2011; Accepted 22 August 2011

Academic Editor: Victor M. Perez Garcia

Copyright © 2011 Simona Fišnarová and Robert Mařík. 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 study the half-linear differential equation ( 𝑟 ( 𝑡 ) Φ ( 𝑥 ) ) + 𝑐 ( 𝑡 ) Φ ( 𝑥 ) = 0 , where Φ ( 𝑥 ) = | 𝑥 | 𝑝 − 2 𝑥 , 𝑝 > 1 . Using the modified Riccati technique, we derive new nonoscillation criteria for this equation. The results are closely related to the classical Hille-Nehari criteria and allow to replace the fixed constants in known nonoscillation criteria by a certain one-parametric expression.