Arbitrarily large solutions of the conformal scalar curvature problem at an isolated singularity
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- by Steven D. Taliaferro and Lei Zhang PDF
- Proc. Amer. Math. Soc. 131 (2003), 2895-2902 Request permission
Abstract:
We study the conformal scalar curvature problem \begin{equation*}k(x) u^{\frac {n+2}{n-2}} \le -\Delta u \le u^{\frac {n+2}{n-2}}\qquad \mathrm {in} \qquad \mathbf {R}^{n},\ n\ge 3,\end{equation*} where $k : \mathbf {R}^{n} \to (0,1]$ is a continuous function. We show that a necessary and sufficient condition on $k$ for this problem to have $C^{2}$ positive solutions which are arbitrarily large at $\infty$ is that $k$ be less than 1 on a sequence of points in $\mathbf {R}^{n}$ which tends to $\infty$.References
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Additional Information
- Steven D. Taliaferro
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- Email: stalia@math.tamu.edu
- Lei Zhang
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- Email: lzhang@math.tamu.edu
- Received by editor(s): March 1, 2002
- Received by editor(s) in revised form: April 11, 2002
- Published electronically: January 28, 2003
- Communicated by: Bennett Chow
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2895-2902
- MSC (2000): Primary 35J60, 53C21
- DOI: https://doi.org/10.1090/S0002-9939-03-06932-6
- MathSciNet review: 1974347