Abstract and Applied Analysis
Volume 2004 (2004), Issue 12, Pages 1019-1030
doi:10.1155/S1085337504404023

Symmetry and concentration behavior of ground state in axially symmetric domains

Abstract

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.