Abstract and Applied Analysis
Volume 2004 (2004), Issue 12, Pages 1019-1030

Symmetry and concentration behavior of ground state in axially symmetric domains

Tsung-Fang Wu

Center for General Education, Southern Taiwan University of Technology, Tainan 71005, Taiwan

Received 9 October 2003

Copyright © 2004 Tsung-Fang Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We let Ω(r) be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground-state solutions of the semilinear elliptic equation in Ω(r) are nonaxially symmetric and concentrative on one side. Furthermore, we prove the necessary and sufficient condition for the symmetry of ground-state solutions.