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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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