Variational method based on finite dimensional approximation in a generalized prescribed mean curvature problem

An elementary existence proof based on variational and finite dimensional approximation methods is proposed for nontrivial solutions of the generalized prescribed mean curvature boundary value problem{−div{[α(x)+|∇u|γ]1γ−1|∇u|γ−2∇u}=f(x,u)in Ω,u=0on ∂Ω, which has been studied otherwise by elaborated abstract theories.