Asymptotic formula for oscillatory solutions of some singular nonlinear differential equation (Q554974)

Summary: The singular differential equation \[ (p(t)u')' = p(t)f(u) \] is investigated. 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 \(p(0) = 0\). An asymptotic formula for oscillatory solutions is derived.