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Liouville-Type Theorems for Conformal Gaussian Curvature Equations in R^2

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摘要 In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions. In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions.
作者 YunYanYANG
机构地区 LMAM
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第1期63-68,共6页 数学学报(英文版)
关键词 Gaussian curvature Total curvature Obata type identity Gaussian curvature Total curvature Obata type identity
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参考文献6

  • 1Cheng, K., Ni, W.: On the structure of the conformal Gaussian curvature equation on R^2 I. Duke Math.J., 62, 721-737 (1991). 被引量:1
  • 2Cheng, K., Ni, W.: On the structure of the conformal Gaussian curvature equation on R^2 Ⅱ. Math. Ann.,290, 671-680 (1991). 被引量:1
  • 3Cheng, K.: On the structure of the conformal Gaussian curvature equation on R^2 Ⅲ. Preprint. 被引量:1
  • 4Lin, C.: Liouville-type theorems for semilinear elliptic equations involving the soblev exponent. Math. Z.,228, 723-744 (1998). 被引量:1
  • 5Cheng, K., Lin, C.: On the asymptotic behavior of solutions of the conformal Gaussian curvature equationsin R^2. Math. Ann., 308, 119-139 (1997). 被引量:1
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