Abstract
We consider two-point boundary-value problems for a Hamiltonian system of the form x′ = f(k, y), y′ = g(x, 𝜆), where k and 𝜆 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 𝜆:
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