Multiple boundary peak solution for critical elliptic system with Neumann boundary condition

We consider the following elliptic system with Neumann boundary condition:$\{\begin{array}{cc}-\Delta u+\mu u=v^p,& \text{in }\Omega ,\\ -\Delta v+\mu v=u^q,& \text{in }\Omega ,\\ \frac{\partial u}{\partial n}=\frac{\partial v}{\partial n}=0,& \text{on }\partial \Omega ,\\ u>0,v>0,& \text{in }\Omega ,\end{array}$ where $\Omega \subset R^N$ is a smooth bounded domain, μ is a positive constant and $(p,q)$ lies in the critical hyperbola:$\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}.$ By using the Lyapunov-Schmidt reduction technique, we establish the existence of infinitely many solutions to above system. These solutions have multiple peaks that are located on the boundary ∂Ω. Our results show that the geometry of the boundary ∂Ω, especially its mean curvature, plays a crucial role on the existence and the behaviour of the solutions to the problem.