Abstract and Applied Analysis
Volume 2011 (2011), Article ID 981401, 9 pages
http://dx.doi.org/10.1155/2011/981401
Research Article

Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation

Irena Rachůnková and Lukáš Rachůnek

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

Received 28 October 2010; Revised 31 March 2011; Accepted 2 May 2011

Academic Editor: Yuri V. Rogovchenko

Copyright © 2011 Irena Rachůnková and Lukáš Rachůnek. 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

Singular differential equation ( 𝑝 ( 𝑡 ) 𝑢 ) = 𝑝 ( 𝑡 ) 𝑓 ( 𝑢 ) is investigated. 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 . An asymptotic formula for oscillatory solutions is derived.