Nodal ground state solution to a biharmonic equation via dual method

Using dual method we establish the existence of nodal ground state solution for the following class of problems $$\left\{ \begin{array}{l} \Delta^2 u = f(u), \quad \mbox{in} \quad \Omega, \\ u =Bu=0,\quad\mbox{on} \quad \partial \Omega \end{array} \right.$$ where $\Delta^2$ is the biharmonic operator, $B=\Delta$ or $B=\dfrac{\partial}{\partial \nu}$ and $f$ is a $C^1$-function having subcritical growth.