A Variational Principle for Eigenvalue Problems of Hamiltonian Systems
  We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the bifurcating branch $\lambda$ as a function of the amplitude of the solution. As an application we show how it can be used to obtain simple approximate closed formulae for the period of large amplitude oscillations. 
R. D. Benguria and M. C. Depassier (Facultad de Fisica, Universidad   Catolica de Chile, Santiago, Chile)