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

Author(s): Sanxing Wu; Hongying Liu
Journal: Proc. Amer. Math. Soc. 132 (2004), 3083-3088.
MSC (2000): Primary 53C21; Secondary 35J60
Posted: May 12, 2004
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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: 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
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society

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