Electronic Research Announcements

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

Author(s): L. Brandolini; M. Rigoli; A. G. Setti
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 101-107.
MSC (1991): Primary 35H05; Secondary 35J70
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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.

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Retrieve articles in Electronic Research Announcements with MSC (1991): 35H05, 35J70

L. Brandolini
Affiliation: Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy
Email: brandolini@vmimat.mat.unimi.it

M. Rigoli
Affiliation: Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy
Email: rigoli@vmimat.mat.unimi.it

A. G. Setti
Affiliation: Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy
Email: setti@vmimat.mat.unimi.it

DOI: 10.1090/S1079-6762-96-00014-5
PII: S 1079-6762(96)00014-5
Keywords: Heisenberg group, hypoelliptic equations, CR-Yamabe problem
Received by editor(s): March 8, 1996
Communicated by: Richard Schoen
Copyright of article: Copyright 1997, American Mathematical Society

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