Abstract
The aim of this chapter is to prove some uniqueness results for positive solutions of Yamabe-type equations. Our first theorem in this direction depends only on the sign of the coefficient \( b(x) \) of the nonlinear term and, loosely speaking, on an \( L^2 \)-type estimate of the distance, at infinity, of the two solutions under consideration. It is worth observing that this very general result is sharp and that the \( L^2 \)-type condition cannot be substituted with a corresponding \( L^p \) condition with \( p > 2 \)
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© 2012 Springer Basel
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Mastrolia, P., Rigoli, M., Setti, A.G. (2012). Uniqueness. In: Yamabe-type Equations on Complete, Noncompact Manifolds. Progress in Mathematics, vol 302. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0376-2_5
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DOI: https://doi.org/10.1007/978-3-0348-0376-2_5
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0375-5
Online ISBN: 978-3-0348-0376-2
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