Multiple solutions of boundary-value problems for Hamiltonian systems - Kirichuka, A. (Нелінійні коливання, 2017)
We consider two-point boundary-value problems for Hamiltonian system of the form x' = f(k, y), y' = g(x, λ), where k and λ are parameters. We estimate the number of solutions, both positive and oscillatory, for the boundary-value problems. Our main tool is the phase plane analysis combined with evaluations of time map functions. The bifurcation diagram and solution curves for Hamiltonian system are constructed. Examples are considered illustrating bifurcations with respect to the parameters k and λ.