Ground state for critical elliptic systems with perturbation term of superlinear type

This work deals with the existence of at least one positive ground state solution for a stationary perturbed critical elliptic system with superlinear potential. Our problems involve the critical Sobolev constants which generate the lack of compactness in unbounded domains; we overcome such difficulty by using the concept of the Palais- Smale convergence. We make recourse to the Ekeland variational principle to show that our problem has a positive time-independent solution with positive energy as the total energy of the system.