  In this paper we prove the nonexistence of nontrivial solution to
\begin{equation*} \begin{cases} -\Delta u =f(u) &\text{in }\Omega, \\ u=0
&\text{on } \partial \Omega, \end{cases} \end{equation*} being $\Omega \subset
\mathbb{R}^N$ ($N\in \mathbb{N}$) a bounded domain and $f$ locally Lispchitz
with non-positive primitive.
