Some existence results of bounded variation solutions to 1-biharmonic problems

In this paper we establish some existence results to a fourth-order quasilinear elliptic equation involving the 1-biharmonic operator, formally given by Δ12u=Δ(Δu|Δu|). We consider different geometrical assumptions in the nonlinearity and use variational methods in order to get nontrivial ground-state solutions.