Existence of multiple solutions for a fourth-order problem with variable exponent

We provide a new multiplicity result for a weighted \begin{document}$ p(x) $\end{document} -biharmonic problem on a bounded domain \begin{document}$ \Omega $\end{document} of \begin{document}$ \mathbb R^n $\end{document} with Navier conditions on \begin{document}$ \partial\Omega $\end{document} . Our approach, of variational nature, requires a suitable oscillating behavior of the nonlinearity and the associated weight to be compactly supported in \begin{document}$ \Omega $\end{document} .