Solvability of the fourth order nonlinear subelliptic equations on the Heisenberg group. (Q1812217)

The paper proposes some existence results (via variational approach) for fourth order semilinear subelliptic equations on the Heisenberg groups \[ \begin{cases} \Delta^2_Hu+c\Delta_Hu=f((z,t),u)\quad \text{ in}\;D,\\ u| _{\partial D}=\Delta_Hu| _{\partial D}=0 \end{cases} \] where \(D\) is a bounded open subset of the Heisenberg group \(H^n\) and \(\Delta_H\) is the subelliptic Laplacian on \(H^n.\)