  For $N\geq 4$, we let $\Omega$ be a bounded domain of $\mathbb{R}^N$ and
$\Gamma$ be a closed curve contained in $\Omega$. We study existence of
positive solutions $u \in H^1_0\left(\Omega\right)$ to the equation
\begin{equation}\label{Atusi} -\Delta u+hu=\lambda\rho^{-s_1}_\Gamma
u^{2^*_{s_1}-1}+\rho^{-s_2}_\Gamma u^{2^*_{s_2}-1} \qquad \textrm{ in } \Omega
\end{equation} where $h$ is a continuous function and $\rho_\Gamma$ is the
distance function to $\Gamma$. We prove the existence of a mountain pass
solution for this Euler-Lagrange equation depending on the local geometry of
the curve and the potential $h$.
