On a critical Hamiltonian system with Neumann boundary conditions

We consider the Hamiltonian system with Neumann boundary conditions: \[ -Δ u + μ u=vq, -Δ v+ μ v=uᵖ in Ω, u, v >0 in Ω, ∂_ν u= ∂_ν v=0 on ∂ Ω, \] where μ >0 is a parameter and Ω is a smooth bounded domain in RN . When $(p, q)$ approaches from below the critical hyperbola $N/(p+1) + N/(q+1)=N-2$, we build a solution which blows-up at a boundary point where the mean curvature achieves its minimum and negative value.