A Variational Principle for Eigenvalue Problems of Hamiltonian Systems
Abstract
We consider the bifurcation problem
u
′′
+λu=N(u)
with two point boundary conditions where
N(u)
is a general nonlinear term which may also depend on the eigenvalue
λ
. We give a variational characterization of the bifurcating branch
λ
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.