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Abstract and Applied Analysis
Volume 2012, Article ID 787920, 18 pages
Research Article

On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation

1Division of Network, Vodafone Spain S. A., P. E. Castellana Norte, 28050 Madrid, Spain
2Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Received 11 September 2012; Revised 12 November 2012; Accepted 28 November 2012

Academic Editor: Ferhan Atici

Copyright © 2012 Pedro Almenar and Lucas Jódar. 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.


This paper presents two methods to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second-order half-linear differential equation , with and piecewise continuous and , and being real such that . It also compares between them in several examples. Lower bounds (i.e., Lyapunov inequalities) for such a distance are also provided and compared with other methods.