Mass effect on an elliptic PDE involving two Hardy-Sobolev critical exponents

We let $\mathrm{\Omega }$ be a bounded domain of ${\mathbb{R}}^3$ and $\mathrm{\Gamma }$ be a closed curve contained in $\mathrm{\Omega }$. We study existence of positive solutions $u\in H_0^1\left(\mathrm{\Omega }\right)$ to the equation $$-\mathrm{\Delta }u+hu=\lambda {\rho }_{\mathrm{\Gamma }}^{-s_1}{u}^{5-2s_1}+{\rho }_{\mathrm{\Gamma }}^{-s_2}{u}^{5-2s_2}\text{ in }\mathrm{\Omega }$$ where $h$ is a continuous function and ${\rho }_{\mathrm{\Gamma }}$ is the distance function to $\mathrm{\Gamma }$. We prove existence of solutions depending on the regular part of the Green function of linear operator. We prove the existence of positive mountain pass solutions for this Euler-Lagrange equation depending on the mass which is the regular part of the Green function of the linear operator $-\mathrm{\Delta }+h$.