Existence of Periodic Solutions for a Class of Discrete Hamiltonian Systems

Abstract EN

By applying minimax methods in critical point theory, we prove the existence of periodic solutions for the following discrete Hamiltonian systems Δ2u(t-1)+∇F(t,u(t))=0, where t∈ℤ, u∈ℝN, F:ℤ×ℝN→ℝ, F(t,x) is continuously differentiable in x for every t∈ℤ and is T-periodic in t;T is a positive integer.