In this work we give necessary and sufficient conditions for having a maximum principle for cooperative elliptic systems involving p-Laplacian operator on the whole RN . This principle is then used to yield solvability for the cooperative elliptic systems by an approximation method.

Several systems of differential operators are constructed and their study is commenced. These systems are generalizations, in a reasonable sense, of the Heisenberg Laplacian operators introduced by Folland and Stein. In particular, they admit large groups of conformal symmetries; various real form of the special linear groups, even special orthogonal groups, and the exceptional group of type E6...