Variational approach to a class of nonlinear oscillators with several limit cycles

We study limit cycles of nonlinear oscillators described by the equation x + nuF(x) + x = 0 with F an odd function. Depending on the nonlinearity, this equation may exhibit one or more limit cycles. We show that limit cycles correspond to relative extrema of a certain functional. Analytical results in the limits nu-->0 and nu-->infinity are in agreement with previously known criteria. For intermediate nu, numerical determination of the limit cycles can be obtained.