Decay rate of solution to linear elliptic problem

I am interested in solutions $u(x)$ of the following equation: $$-\Delta u(x) = f(x) \qquad R^N,$$ where we assume that $u(x) \rightarrow \infty$ as $|x| \rightarrow \infty$.

I am interested in obtaining estimates of the form

$$\sup (1+|x|^t ) |u(x)| \le C ||f||'$$

where $t>N-2$ and where $\| \cdot \|$ is some appropriate norm.

Note that this will probably require some cancellation in $f$ since if $f$ is nonnegative and compactly supported then using the Newtonian potential expression for $u(x)$ one sees that $u(x)$ is roughly $|x|^{2-N}$ for large $x$.