96-187 Benguria, R. and Depassier, M. C.

A Variational Principle for Eigenvalue Problems of Hamiltonian Systems (106K, postcript file, gzipped and uuencoded) 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.

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