VARIATIONAL PRINCIPLE FOR EIGENVALUE PROBLEMS OF HAMILTONIAN-SYSTEMS

We consider the bifurcation problem u '' + lambda u = N(u) with two po int boundary conditions where N(LI) is a general nonlinear term which may also depend on the eigenvalue lambda. We give a variational charac terization of the bifurcating branch lambda as a function of th amplit ude of the solution. As an application we show how it can be used to o btain simple approximate closed formulas for the period of large ampli tude oscillations.