Critical Neumann problem for nonlinear elliptic systems in exterior domains

In this paper, we investigate the Neumann problem for a critical elliptic system in exterior domains. Assuming that the coefficient $Q(x)$ is a positive smooth function and $lambda$, $mugeq0$ are parameters, we examine the common effect of the mean curvature of the boundary $partial Omega $ and the shape of the graph of the coefficient $Q(x)$ on the existence of the least energy solutions.