Periodic solutions for subquadratic discrete Hamiltonian systems (Q2472249)

The paper is concerned with discrete Hamiltonian systems of the form \[ J\Delta x(n)+\nabla H(nLx(n))=0 , \] where \(x(n)=(x_1(n),x_2(n))^T\), \(\Delta x(n)= x(n+1)-x(n)\), \(Lx(n)=(x_1(n+1),x_2(n))^T\), \(J\) is the standard symplectic matrix, \(\nabla H\) denotes the gradient of \(H\). Some sufficient conditions on the existence of periodic solutions are obtained by the minimax methods of critical point theory.