The author studies the system , with , , where . Here, is a continuous -periodic function, has superquadratic behavior, is a continuous -periodic symmetric matrix function, with , for all , and .
The author shows that if , and then the system has a -periodic solution. With some additional assumptions including (reversing the sign) it also follows that a -periodic solution exists. Using a variational approach, she proves that the corresponding Lagrangian action integral
has a critical point in an appropriately chosen finite subspace of the original Hilbert space .