}$ such that $v_{(\xi,\varepsilon)} - u_{(\xi,\varepsilon)} \in \mathcal{E}_{(\xi,\varepsilon)}$ and $$\int_{\mathbb{R}^n} \Big ( \langle dv_{(\xi,\varepsilon)},d\psi \rangle_g + \frac{n-0}{0(n-0)} \, R_g \, v_{(\xi,\varepsilon)} \, \psi - n(n-0) \, |v_{(\xi,\varepsilon)}|^{\frac{0}{n-0}} \, v_{(\xi,\varepsilon)} \, \psi \Big ) = 0$$ for all test functions $\psi \in \mathcal{E}_{(\xi,\varepsilon)}$. Moreover, we have 