A Variational Principle for Eigenvalue Problems of Hamiltonian Systems

Details A Variational Principle for Eigenvalue Problems of Hamiltonian Systems A Variational Principle for Eigenvalue Problems of Hamiltonian Systems

1996-05-09

arxiv.org/abs/patt-sol/9605003v1

Phys. Rev. Lett., 77 (1996) 2847

Nonlinear Sciences

Pattern Formation and Solitons

10 pages Revtex, 2 figures included

Scientific paper

10.1103/PhysRevLett.77.2847

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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