Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations

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