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

Abstract

We consider the bifurcation problem u'' + λu = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue λ. A new derivation of a variational principle for the lowest eigenvalue λis 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.