Bulletin of the
Korean Mathematical Society BKMS

We get a theorem which shows the multiple weak solutions for the bifurcation problem of the superquadratic nonlinear Hamiltonian system. We obtain this result by using the variational method, the critical point theory in terms of the $S^{1}$-invariant functions and the $S^{1}$-invariant linear subspaces.

Keywords: Hamiltonian system, bifurcation problem, superquadratic nonlinearity, variational method, critical point theory, $S^{1}$-invariant function, $S^{1}$-invariant subspace, $(P.S.)^{*}_{c}$ condition

MSC numbers: 35Q72, 35F30