Nodal ground state solution to a biharmonic equation via dual method

Abstract

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