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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.

35H10 Hypoelliptic equations
35J70 Degenerate elliptic equations
43A80 Analysis on other specific Lie groups
Full Text: DOI EuDML
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