Bulletin of the
Korean Mathematical Society BKMS

We get a theorem which shows the existence of at least four 2$\pi$-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.

Keywords: Hamiltonian system, bifurcation problem, superquadratic nonlinearity, variational method, limit relative category, critical point theory, $(P.S.)^{*}_{c}$ condition

MSC numbers: 35Q70, 35F50