Advances in Difference Equations
Volume 2010 (2010), Article ID 872160, 13 pages
Research Article

Oscillatory Solutions of Singular Equations Arising in Hydrodynamics

1Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, tř. 17. listopadu 12, 771 46 Olomouc, Czech Republic
2VŠB, Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic

Received 26 December 2009; Accepted 29 March 2010

Academic Editor: Josef Diblik

Copyright © 2010 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.


We investigate the singular differential equation (p(t)u(t))=p(t)f(u(t)) on the half-line [0,), where f satisfies the local Lipschitz condition on and has at least two simple zeros. The function p is continuous on [0,) and has a positive continuous derivative on (0,) and p(0)=0. We bring additional conditions for f and p under which the equation has oscillatory solutions with decreasing amplitudes.