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.

Abstract

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 ℝ 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.