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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive solutions of anisotropic Yamabe-type equations in $\mathbb {R}^n$
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by Roberto Monti and Daniele Morbidelli PDF
Proc. Amer. Math. Soc. 136 (2008), 4295-4304 Request permission

Abstract:

We study entire positive solutions to the partial differential equation in $\mathbb {R}^{n}$, \[ \Delta _{x}u + (\alpha + 1)^2 |x|^{2\alpha } \Delta _{y}u = - |x|^{2\alpha } u^{\frac {n+2}{n-2}}, \] 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
  • Received by editor(s): October 19, 2007
  • Published electronically: June 11, 2008
  • Communicated by: Matthew J. Gursky
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2431043