A Lyapunov inequality for a second order nonlinear differential equation (Q617026)

The paper deals with the equation \[ (r(x)y')'+p(x)f(y(x))=0\tag{1} \] with \(r(x),\) \(p(x)>0\) and \(f(y)\) odd and positive for \(y>0.\) Using a Lyapunov-type inequality, the author gives estimates of the distance between a zero of the solution \(y(x)\) of (1) and the immediately former or latter zero of its derivative \(y'(x).\)