Existence of oscillatory solutions of singular nonlinear differential equations (Q554896)

Summary: 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 \(\mathbb R\) and has at least two zeros 0 and \(L > 0\). The function \(p\) is continuous on \([0, \infty)\) and has a positive continuous derivative on \((0, \infty)\) and \(p(0) = 0\). Further conditions on \(f\) and \(p\) under which the equation has oscillatory solutions converging to \(0\) are given.