Positive solutions of Yamabe type equations on complete manifolds and applications

Authors
Brandolini, L Rigoli, M Setti, AG
Citation
L. Brandolini et al., Positive solutions of Yamabe type equations on complete manifolds and applications, J FUNCT ANA, 160(1), 1998, pp. 176-222
Citations number
22
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN journal
00221236 → ACNP
Volume
160
Issue
1
Year of publication
1998
Pages
176 - 222
Database
ISI
SICI code
0022-1236(199812)160:1<176:PSOYTE>2.0.ZU;2-W
Abstract
We study the semilinear equation Delta u + a(x)u = b(x)u(sigma) (sigma > 1) on a complete Riemannian manifold. We determine conditions on the coeffici ents that guarantee existence and nonexistence of positive solutions. A ver y general uniqueness result is also established. Our main results are valid without explicit curvature assumptions, and appear to be new even in R-m. (C) 1998 Academic Press.