Some existence results of bounded variation solutions to 1-biharmonic problems - Barile, Sara; Pimenta, Marcos T.O. [UNESP] (Elsevier, 2018)
In this paper we establish some existence results to a fourth-order quasilinear elliptic equation involving the 1-biharmonic operator, formally given by Δ1 2u=Δ([Formula presented]). We consider different geometrical assumptions in the nonlinearity and use variational methods in order to get nontrivial ground-state solutions.
Keywords: 1-biharmonic operator; Bounded variation functions; Variational methods