Abstract and Applied Analysis
Volume 2011 (2011), Article ID 408525, 20 pages
http://dx.doi.org/10.1155/2011/408525
Research Article

Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations

Irena Rachůnková, Lukáš Rachůnek, and Jan Tomeček

Department of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic

Received 10 October 2010; Revised 25 February 2011; Accepted 23 March 2011

Academic Editor: Yuri V. Rogovchenko

Copyright © 2011 Irena Rachůnková 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

Asymptotic properties of solutions of the singular differential equation ( 𝑝 ( 𝑡 ) 𝑢 ( 𝑡 ) ) = 𝑝 ( 𝑡 ) 𝑓 ( 𝑢 ( 𝑡 ) ) are described. Here, f is Lipschitz continuous on ℝ and has at least two zeros 0 and 𝐿 > 0 . The function p is continuous on [0, ∞ ) and has a positive continuous derivative on (0, ∞ ) and 𝑝 ( 0 ) = 0 . Further conditions for f and p under which the equation has oscillatory solutions converging to 0 are given.