Pais-Uhlenbeck Oscillator with a Benign Friction Force

It is shown that the Pais-Uhlenbeck oscillator with damping, considered by Nesterenko, is a special case of a more general oscillator that has not only a first order, but also a third order friction term. If the corresponding damping constants, \alpha\ and \beta, are both positive and below certain critical values, then the system is stable. In particular, if \alpha = - \beta, then we have the unstable Nesterenko's oscillator