MULTIPLE SOLUTIONS OF BOUNDARY-VALUE PROBLEMS FOR HAMILTONIAN SYSTEMS

摘要

We consider two-point boundary-value problems for a Hamiltonian system of the form x′ = f ( k, y ), y′ = g(x , ğœ†), where k and 𜆠are parameters. The numbers of solutions, both positive and oscillatory, for the boundary-value problems are estimated. Our main tool is the analysis of the phase plane combined with the evaluation of time-map functions. The bifurcation diagram and solution curves are constructed for the Hamiltonian system. We also present examples illustrating the bifurcations with respect to the parameters k and ğœ†:.