Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems

Details Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems

1997-06-10

arxiv.org/abs/patt-sol/9706002v1

Nonlinear Sciences

Pattern Formation and Solitons

2 pages, Revtex, no figures

Scientific paper

10.1016/S0375-9601(98)00100-5

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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