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

摘要

In this paper we establish some existence results to a fourth-order quasilinear elliptic equation involving the 1-biharmonic operator, formally given by Delta(2)(1)u = Delta(Delta u/|Delta u)). We consider different geometrical assumptions in the nonlinearity and use variational methods in order to get nontrivial ground-state solutions. (C) 2018 Elsevier Inc. All rights reserved.