Symmetry of Solutions of Systems of Semilinear Elliptic Equations

• Main Authors: Yu-Yuan Hung, 洪裕元
• Other Authors: Chiun-Chuan Chen
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/92273431168274156256

碩士 === 國立臺灣大學 === 數學研究所 === 88 === In this paper, we are interested in the symmetry of solutions of systems os semilinear elliptic equations. We follow the results discovered by Berestycki, H. and Nirenberg, L. and generalize to systems of semilinear elliptic equations. By using the method of moving planes, we can get the symmetry in some direction for solutions of systems of semilinear elliptic equations in a bounded domain which is convex in that direction. Furthermore, if the domain is a ball and the solution (u,v) is radially symmetric, then we can find some relation between u and v. If we apply this relation to the original system of semilinear elliptic equations, it can be reduced to a single elliptic equation. So if this reduced single elliptic equation has no solutions, we are sure that the original system of semilinear elliptic equations has no radially symmetric solutions.