On Nonlinear Biharmonic Problems on the Heisenberg Group (original) (raw)

We investigate the boundary value problem for biharmonic operators on the Heisenberg group. The inherent features of Hn make it an appropriate environment for studying symmetry rules and the interaction of analysis and geometry with manifolds. The goal of this paper is to prove that a weak solution for a biharmonic operator on the Heisenberg group exists. Our key tools are a version of the Mountain Pass Theorem and the classical variational theory. This paper will be of interest to researchers who are working on biharmonic operators on Hn.