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Positive solutions of anisotropic Yamabe-type equations in $ \mathbb{R}^n$


Authors: Roberto Monti and Daniele Morbidelli
Journal: Proc. Amer. Math. Soc. 136 (2008), 4295-4304
MSC (2000): Primary 35J60; Secondary 35J70
DOI: https://doi.org/10.1090/S0002-9939-08-09579-8
Published electronically: June 11, 2008
MathSciNet review: 2431043
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Abstract | References | Similar Articles | Additional Information

Abstract: We study entire positive solutions to the partial differential equation in $ \mathbb{R}^{n}$,

$\displaystyle \Delta_{x}u + (\alpha + 1)^2 \vert x\vert^{2\alpha} \Delta_{y}u = - \vert x\vert^{2\alpha} u^{\frac{n+2}{n-2}}, $

where $ x\in\mathbb{R}^2$, $ y\in\mathbb{R}^{n-2}$, $ n\geq 3$ and $ \alpha > 0$. We classify positive solutions with second order derivatives satisfying a suitable growth near the set $ x=0$.


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Additional Information

Roberto Monti
Affiliation: Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste, 63, 35121 Padova, Italy
Email: monti@math.unipd.it

Daniele Morbidelli
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, 40127 Bologna, Italy
Email: morbidel@dm.unibo.it

DOI: https://doi.org/10.1090/S0002-9939-08-09579-8
Received by editor(s): October 19, 2007
Published electronically: June 11, 2008
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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