Periodic solution for Hamiltonian type systems with critical growth

We consider an elliptic system of Hamiltonian type in a strip in R N , satisfying the periodic boundary condition for the first k variables. In the superlinear case with critical growth, we prove the existence of a single bubbling solution for the system under an optimal condition on k . The novelty of the paper is that all the estimates needed in the proof of the existence result can be obtained once the Green’s function of the Laplacian operator in a strip with periodic boundary conditions is found.