Symmetry Breaking for a Class of Semi-Linear Elliptic Problems

摘要

This document considers a nonlinear elliptic problem. Suppose this problem has a family of positive radial solutions parameterized by R, i.e., UR (X). This paper studies the possibility of the existence of nonradial solutions of bifurcating from the radial solutions family. Answering a question posed by Smoller and Wasserman, it is shown this happens if f satisfies suitable assumptions. Therefore, the global structure of the nonradial solution set is investigated.