Remark on Gauss curvature equations on punctured disk

Yuxiang LI , Hongyan TANG

Front. Math. China ›› 2020, Vol. 15 ›› Issue (4) : 701 -707.

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Front. Math. China ›› 2020, Vol. 15 ›› Issue (4) : 701 -707. DOI: 10.1007/s11464-020-0855-8
RESEARCH ARTICLE
RESEARCH ARTICLE

Remark on Gauss curvature equations on punctured disk

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Abstract

We give a new argument on the classification of solutions of Gauss curvature equation on R2; which was first proved by W. Chen and C. Li [Duke Math. J., 1991, 63(3): 615–622]. Our argument bases on the decomposition properties of the Gauss curvature equation on the punctured disk.

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Gauss curvature equation / singular point

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Yuxiang LI, Hongyan TANG. Remark on Gauss curvature equations on punctured disk. Front. Math. China, 2020, 15(4): 701-707 DOI:10.1007/s11464-020-0855-8

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References

[1]

Brezis H, Merle F. Uniform estimates and blow-up behavior for solutions of −Δu= V (x)eu in two dimensions. Comm Partial Differential Equations, 1991, 16: 1223–1253

[2]

Chen W, Li C. Classification of solutions of some nonlinear elliptic equations. Duke Math J, 1991, 63(3): 615–622

[3]

Chou K, Wan Y. Asymptotic radial symmetry for solutions of Δu+ eu= 0 in a punctured disc. Pacific J Math, 1994, 163(2): 269{276

[4]

Struwe M. Positive solutions of critical semilinear elliptic equations on non-contractible planar domains. J Eur Math Soc (JEMS), 2000, 2(4): 329–388

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