Let $M := C_0^{\infty}(\mathbb{R}^n)$ denote the smooth maps with compact support. Then we have a map
$\Delta:M\rightarrow M,\,\, f\mapsto \Delta f$,
where $\Delta f = \sum_{i=1}^{n} \frac{\partial^2}{\partial x_i^2}f$ is the Laplacian. I am wondering if $\Delta$ is surjective, i.e. if for any $f\in M$ there exists an $F\in M$ with $\Delta F = f$. Is that true?
Thanks for your help!