Symmetry breaking of an elliptic equation in expanding annuli

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• 作者：Zongming Guo ; Linfeng Mei ; Fangshu Wan
• 关键词：Expanding annuli ; Bifurcation ; Symmetry breaking ; Morse index ; Supercritical exponent
• 刊名：NoDEA : Nonlinear Differential Equations and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：23
• 期：6
• 全文大小：646 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9004
• 卷排序：23

文摘

We obtain non-radial bifurcation from radial solutions of a semilinear elliptic equation in expanding annuli of \(\mathbb {R}^N\). To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equation $$\begin{aligned} -\Delta u=\lambda u^p \quad \text {in}\quad \mathbb {R}^N. \end{aligned}$$ (0.1)The main results of this paper can be seen as applications of the properties of regular entire solutions of (0.1).KeywordsExpanding annuliBifurcationSymmetry breakingMorse indexSupercritical exponentResearch of the first author is supported by NSFC (11171092, 11571093); Research of the second author is supported by NSFC (11371117).