On the Singular Solutions of .DELTA.u + K(x)exp(2u) = 0 in .R^2.

• Main Authors: Chen, Shyh Huei, 陳世輝
• Other Authors: Cheng, Kuo Shung
• Format: Others
• Language: en_US
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/90323664543080751952

碩士 === 國立中正大學 === 應用數學研究所 === 81 === In this paper we investigate the conformal Gaussian curvature equation (P.D.E.) : .DELTA.u + K(x)exp(2u) = 0 in .R^2. When K is radially symmetric and radial solutions u are seeked, above equation can be reduced to an ordinary differential (O.D.E.) : u''(r) + 1/r u'(r) + K(r) exp(2u) =0, r>0. In theis paper we are interested in the singular solutions u of (O.D.E.) having following asymptotic behaviors: u(r) = a log(r) + .alpha. + o(1) as r .arrr. 0 u(r) = b log(r) + o(log(r)) as r .arrr. .inf. We shall give some examples which the exact solutions can be written down explicitly. These examples indicate us theof b upon a and .alpha. . And we shall plot numberically the dependence of b on .alpha. for a=0.17