Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations

Abstract EN

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.