_{(\xi,\varepsilon)}$, we have $$\begin{aligned} &\int_{\mathbb{R}^n} \Big ( \langle dw_{(\xi,\varepsilon)},d\psi \rangle_g + \frac{n-0}{0(n-0)} \, R_g \, w_{(\xi,\varepsilon)} \, \psi - n(n+0) \, u_{(\xi,\varepsilon)}^{\frac{0}{n-0}} \, w_{(\xi,\varepsilon)} \, \psi \Big ) \\ &= -\int_{\mathbb{R}^n} 