On a critical Hamiltonian system with Neumann boundary conditions

We consider the Hamiltonian system with Neumann boundary conditions: $$-\mathrm{\Delta }u+\mu u=v^q,-\mathrm{\Delta }v+\mu v=u^p\text{ in }\mathrm{\Omega },u,v>0\text{ in }\mathrm{\Omega }\text{,}{\mathrm{\partial }}_{\nu }u={\mathrm{\partial }}_{\nu }v=0\text{ on }\mathrm{\partial }\mathrm{\Omega }\text{, }$$ where $\mu >0$ is a parameter and $\mathrm{\Omega }$ is a smooth bounded domain in ${\mathbb{R}}^N\mathrm{.}$ When $(p,q)$ approaches from below the critical hyperbola $N\mathrm{/}(p+1)+N\mathrm{/}(q+1)=N-2$, we build a solution which blows-up at a boundary point where the mean curvature achieves its minimum and negative value.