A Variational Principle for Eigenvalue Problems of Hamiltonian Systems

Abstract

We consider the bifurcation problem $u^{\prime \prime }+\lambda u=N(u)$ 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.

10 pages Revtex, 2 figures included

References in corpus (2)

• The Speed of Fronts of the Reaction Diffusion Equation
• Variational Characterization of the Speed of Propagation of Fronts for the Nonlinear Diffusion Equation

Cited by in corpus (5)

• Variational approach to a class of nonlinear oscillators with several limit cycles
• Variational calculation of the period of nonlinear oscillators
• Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems
• A comparative study of some analytic approximate methods for the anharmonic oscillator described by cubic quartic potential
• On the principal bifurcation branch of a third order nonlinear long-wave equation