Variational calculation of the period of nonlinear oscillators
  The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and lower bounds on the period can be obtained to any desired degree of accuracy. The results are illustrated by an application to the Duffing equation. 
R. D. Benguria, M. C. Depassier