- 96-187 Benguria, R. and Depassier, M. C.
- A Variational Principle for Eigenvalue Problems of
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May 10, 96
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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.