  In this paper, we establish existence, uniqueness, and scale-invariant
estimates for fundamental solutions of non-homogeneous second order elliptic
systems with bounded measurable coefficients in $\mathbb{R}^n$ and for the
corresponding Green functions in arbitrary open sets. We impose certain
non-homogeneous versions of de Giorgi-Nash-Moser bounds on the weak solutions
and investigate in detail the assumptions on the lower order terms sufficient
to guarantee such conditions.
