Multiple Periodic Solutions for Odd Perturbations of the Discrete Relativistic Operator

We obtain the existence of multiple pairs of periodic solutions for difference equations of type -Delta(Delta u(n-1) /root 1-vertical bar Delta u(n-1)vertical bar(2)) = lambda g(u(n)) (n is an element of Z), where g : R -> R is a continuous odd function with anticoercive primitive, and lambda > 0 is a real parameter. The approach is variational and relies on the critical point theory for convex, lower semicontinuous perturbations of C-1-functionals.