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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 a generalised Díaz-Saá inequality. Using these we derive a comparison principle and uniqueness of positive solutions to nonlinear hypoelliptic equations on general stratified Lie groups extending to this setting previously known 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