Min-max level estimate for a singular quasilinear polyharmonic equation   in $\mathbb{R}^{2m}$
  Using the framework first presented by Ruf and Sani, we give a proof of an Adams type inequality which can be applied to a nonlinear functional. Under two kinds of assumptions on the nonlinearity, we estimate the min-max level of the functional. As an application, a multiplicity result for the related singular quasilinear elliptic equation is proved. 
Liang Zhao, Yuanyuan Chang
math.AP