On the existence of positive solutions of Yamabe-type equations on the Heisenberg group

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On the existence of positive solutions of Yamabe-type equations on the Heisenberg group

L. Brandolini, M. Rigoli and A. G. Setti

Abstract.

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.

Copyright American Mathematical Society 1997

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Article Info

ERA Amer. Math. Soc. 02 (1996), pp. 101-107
Publisher Identifier: S 079-6762(96)00014-5
1991 Mathematics Subject Classification. Primary 35H05; Secondary 35J70
Key words and phrases. Heisenberg group, hypoelliptic equations, CR-Yamabe problem
Received by the editors March 8, 1996
Communicated by Richard Schoen
Comments (When Available)

L. Brandolini

Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy

E-mail address: brandolini@vmimat.mat.unimi.it

M. Rigoli

Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy

E-mail address: rigoli@vmimat.mat.unimi.it

A. G. Setti

Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy

E-mail address: setti@vmimat.mat.unimi.it

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