Benguria, R. and Depassier, M. C.
A Variational Principle for Eigenvalue Problems of
Hamiltonian Systems
(106K, postcript file, gzipped and uuencoded)
ABSTRACT. 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.