New existence and multiplicity theorems of periodic solutions for non-autonomous second order Hamiltonian systems (Q2472637)

The authors deal with the non-autonomous second-order Hamiltonian systems \[ u''(t)=\nabla F(t, u(t))\quad\text{a.e.}\,t\in [0,T], \quad u(0)- u(T)= u'(0)- u'(T)= 0, \] where \(T> 0\) and \(F: [0,T]\times \mathbb R^N\to\mathbb R\) satisfies some natural assumptions. They give a new existence theorem and multiplicity theorem.