Analytic study on backreacting holographic superconductors with dark   matter sector
  The variational method for Sturm-Liouville eigenvalue problem was employed to study analytically properties of the holographic superconductor with dark matter sector, in which a coupling between Maxwell field and another U(1)-gauge field was considered. The backreaction of the dark matter sector on gravitational background in question was also examined. 
Lukasz Nakonieczny and Marek Rogatko
hep-th gr-qc