Multiple Periodic Solutions for Odd Perturbations of the Discrete Relativistic Operator

Abstract

We obtain the existence of multiple pairs of periodic solutions for difference equations of type −Δ(Δu(n − 1)1 − |Δu(n − 1)|2)=λg(u(n))(n∈Z), where g:R→R is a continuous odd function with anticoercive primitive, and λ>0 is a real parameter. The approach is variational and relies on the critical point theory for convex, lower semicontinuous perturbations of C1-functionals.

Keywords

• discrete relativistic operator
• periodic solution
• critical point
• genus