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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the elliptic equation $\Delta u+K(x)e^{2u}=0$ on $B^2$


Authors: Sanxing Wu and Hongying Liu
Journal: Proc. Amer. Math. Soc. 132 (2004), 3083-3088
MSC (2000): Primary 53C21; Secondary 35J60
Published electronically: May 12, 2004
MathSciNet review: 2063130
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Abstract: In this paper we consider the existence problem for the elliptic equation $ \Delta u+K(x)e^{2u}=0$ on $B^2=\{x \in R^2 \mid \vert x\vert<1\}$, which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.


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Additional Information

Sanxing Wu
Affiliation: Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, People’s Republic of China

Hongying Liu
Affiliation: Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, People’s Republic of China
Email: liuhongying@263.sina.com

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07366-6
PII: S 0002-9939(04)07366-6
Keywords: Semilinear elliptic PDE, Gaussian curvature, conformal Riemannian metric
Received by editor(s): January 6, 2003
Received by editor(s) in revised form: May 3, 2003
Published electronically: May 12, 2004
Additional Notes: The first author was supported in part by the China National Education Committee Science Research Foundation
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2004 American Mathematical Society