Phase space derivation of a variational principle for one-dimensional Hamiltonian systems

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. (C) 1998 Published by Elsevier Science B.V.