Periodic solutions of superlinear convex autonomous Hamiltonian systems (Q5928202)

This paper deals with Hamiltonian systems in infinite dimensional (real) Hilbert spaces. The authors prove an existence theorem for periodic solutions: For certain linear Hamiltonian systems with uniformly convex Hamiltonian function there exist a nontrivial \(T\)-periodic orbit for any given \(T>0\). The proof uses a variant of the ``mountain pass theorem'' and the dual least action principle.