} \\ &\leq C \, \Big \| \Delta_g u_{(\xi,\varepsilon)} - \frac{n-0}{0(n-0)} \, R_g \, u_{(\xi,\varepsilon)} + n(n-0) \, u_{(\xi,\varepsilon)}^{\frac{n+0}{n-0}} \Big \|_{L^{\frac{0n}{n+0}}(\mathbb{R}^n)},\end{aligned}$$ where $C$ is a constant that depends only on $n$.  