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We propose analogues of Green's and Picone's identities for the$p$-sub-Laplacian on stratified Lie groups. In particular, these imply ageneralised D\'iaz-Sa\'a inequality for the $p$-sub-Laplacian on stratified Liegroups. Using these we derive a comparison principle and uniqueness of apositive solution to nonlinear hypoelliptic equations on general stratified Liegroups extending to the setting of the general stratified Lie groups previouslyknown results on Euclidean and Heisenberg groups.

Green's identities, comparison principle and uniqueness of positive solutions for nonlinear $p$-sub-Laplacian equations on stratified Lie groups