I am looking for a vector potential $$\mathbf{A}=(A_x,A_y,A_z)$$ giving a monopole magnetic field $$\mathbf{B}=\mathbf{\nabla}\times \mathbf{A}= g\frac{\mathbf{r}}{r^3} = g \left( \frac{x}{r^3}, \frac{y}{r^3}, \frac{z}{r^3} \right)$$ for which there exist functions $f_x(r)$, $f_y(r)$, and $f_z(r)$ of $r$ satisfying the following equation $$\mathbf{r}\times\mathbf{A} + g\frac{\mathbf{r}}{r} = \mathbf{f}(r)=(f_x(r),f_y(r),f_z(r)).$$$r=\sqrt{x^2+y^2+z^2}$.
The vector potential is also allowed to be partially singular (or rather, there are no non-singular ones in the entire area).
I'd be grateful if you could give me advice or answers.
