dorsal/arxiv
View SchemaPhase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems
| Authors | R. D. Benguria, M. C. Depassier |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9706002 |
| URL | https://arxiv.org/abs/patt-sol/9706002 |
| DOI | 10.1016/S0375-9601(98)00100-5 |
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. A new derivation of a variational principle for the lowest eigenvalue \lambda is given. This derivation makes use only of simple algebraic inequalities and leads directly to a more explicit expression for the eigenvalue than what had been given previously.
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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. A new derivation of a variational principle\nfor the lowest eigenvalue \\lambda is given. This derivation makes use only of\nsimple algebraic inequalities and leads directly to a more explicit expression\nfor the eigenvalue than what had been given previously.",
"arxiv_id": "patt-sol/9706002",
"authors": [
"R. D. Benguria",
"M. C. Depassier"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/S0375-9601(98)00100-5",
"title": "Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems",
"url": "https://arxiv.org/abs/patt-sol/9706002"
},
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