Existence Result for a Class of Nonlinear Elliptic Systems on Punctured Unbounded Domains

We establish the existence of a nontrivial solution for systems with an arbitrary number of coupled Poisson equations with critical growth in punctured unbounded domains. The proof depends on a generalized linking theorem due to Krysewski and Szulkin, and on a concentration-compactness argument, proved by Frigon and the author. Applications to reaction-diffusion systems with skew gradient structure are also discussed in the last section.