Analytical Solution to a linear PDE with delta function like source term

Question

I have a time-independent Vlasov equation with source term in $R^2$: $$v\cdot\partial{f}/\partial{x}+\partial{f}/\partial{v}=s(x,v)$$ where $s(0,0)=500$, else $s(x,v)=0$. And I was wondering how to achieve the analytical solution for this PDE because the source term is not the pure delta function(which value should be infinity).