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On the existence of positive solutions of Yamabe-type equations on the Heisenberg group. (English) Zbl 0870.35029
Summary: We study nonexistence, existence and uniqueness of positive solutions of the equation $$\Delta_{H^n}u+a(x)u-b(x)u^\sigma =0$$ with $$\sigma >1$$ on the Heisenberg group $$H^n$$. Our results hold, with essentially no changes, also for the Euclidean version of the above equation. Even in this case they appear to be new.

##### MSC:
 35H10 Hypoelliptic equations 35J70 Degenerate elliptic equations 43A80 Analysis on other specific Lie groups
##### Keywords:
CR-Yamabe problem
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##### References:
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