$-\Delta u>0$ if and only if $u>0$ in this pde

Question

Suppose $\Omega$ a smooth domain with $|\Omega|<\infty$. I am studying this problem \begin{cases} \Delta^2u=|u|^{p-1}u\mbox{ in }\Omega,\\ u=\Delta u=0\mbox{ on }\partial\Omega. \end{cases} I would like to check that $-\Delta u>0$ if and only if $u>0$ (In $\Omega$). But I could not and I do not know any result to help me. Is there any property about $\Delta^2u>0$?