A necessary and sufficient condition for the asymptotic stability of the damped oscillator (Q1893070)

The authors are interested in the solution of an old problem ``to find the conditions on the damping coefficient \(h\) of the second order differential equation \(x'' + h(t)x' + k^2x = 0\) guaranteeing the asymptotic stability of the equilibrium \(x = x' = 0\).'' The authors prove by a very interesting method a new necessary and sufficient condition for the asymptotic stability and they deduce the relations between their results and the results of other authors.