dorsal/arxiv
View SchemaA Variational Principle for Eigenvalue Problems of Hamiltonian Systems
| Authors | R. D. Benguria, M. C. Depassier |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9605003 |
| URL | https://arxiv.org/abs/patt-sol/9605003 |
| DOI | 10.1103/PhysRevLett.77.2847 |
| Journal | Phys. Rev. Lett., 77 (1996) 2847 |
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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"abstract": "We consider the bifurcation problem $u\u0027\u0027 + \\lambda u = N(u)$ with two point\nboundary conditions where $N(u)$ is a general nonlinear term which may also\ndepend on the eigenvalue $\\lambda$. We give a variational characterization of\nthe bifurcating branch $\\lambda$ as a function of the amplitude of the\nsolution. As an application we show how it can be used to obtain simple\napproximate closed formulae for the period of large amplitude oscillations.",
"arxiv_id": "patt-sol/9605003",
"authors": [
"R. D. Benguria",
"M. C. Depassier"
],
"categories": [
"patt-sol",
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],
"doi": "10.1103/PhysRevLett.77.2847",
"journal_ref": "Phys. Rev. Lett., 77 (1996) 2847",
"title": "A Variational Principle for Eigenvalue Problems of Hamiltonian Systems",
"url": "https://arxiv.org/abs/patt-sol/9605003"
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