On a discrete fourth order periodic boundary value problem

The authors study the discrete fourth order periodic boundary value problem (Lu)(t) = λf(t,u(t)) + μg(t,u(t)), t∈[1,N]z, Δⁱu(-1) = Δⁱu(N - 1), 1 = 0, 1, 2, 3, where (Lu)(t) = Δ⁴u(t - 2) - Δ(p(t - 1)Δu(t - 1)) + q(t)u(t). By using variational methods and critical point theory, they obtain some criteria for the existence of infinitely many solutions. Several consequences of the main theorems are also presented. One example is included to illustrate the applicability of the results.