Multiple periodic solutions for superquadratic first-order discrete Hamiltonian systems

摘要

Multiple periodic solutions are obtained for superquadratic first-order discrete Hamiltonian systemsΔu1(t)=-Hu2(t,u1(t+1),u2(t)),Δu2(t)=Hu1(t,u1(t+1),u2(t)),by using the minimax methods in critical point theory, where t∈Z, u1,u2∈Rd, H:Z×R2d→R, H(t, x) is continuously differentiable in x for every t∈Z and T-periodic in the first variable.