  We prove the well-posedness of the differential equation $Au=f$ in the
setting of a stratified group $\mathbb{G}$ when the considered second-order
differential operator $A$ can be non-invariant and non-linear. Our approach
follows the Campanato theory of nearness of operators, allowing one to treat
equations with only bounded coefficients, without any regularity assumptions.
Our analysis becomes explicit in the particular case of the Heisenberg group
$\mathbb{H}^n$ of any dimension and on the Euclidean case $\mathbb{R}^n$, where
in the latter case our results also extend the known results by treating the
unbounded domain setting.
