Min–max level estimate for a singular quasilinear polyharmonic equation in R2mR2m

Using the framework first presented by Ruf and Sani, we give a proof of an Adams type inequality which can be applied to the functionalJϵ(u)=12∫R2m(|∇mu|2+∑γ=0m−1aγ(x)|∇γu|2)dx−∫R2mF(x,u)|x|βdx−ϵ∫R2mhudx. 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.