Symmetry Breaking for a Class of Semi-Linear Elliptic Problems.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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.
- Theoretical Mathematics