Symmetry-breaking bifurcation for the one-dimensional Liouville type equation

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Abstract

The two-point boundary value problem for the one-dimensional Liouville type equation {u+λ|x|leu=0,x∈(−1,1),u(−1)=u(1)=0 is considered, where λ>0 and l>0. In this paper, a symmetry-breaking result is obtained by using the Morse index. The problem {u+λ|x|l(u+1)p=0,x∈(−1,1),u(−1)=u(1)=0 is also considered, where λ>0, l>0, p>1 and (p−1)l>4.

Original languageEnglish
Pages (from-to)6953-6973
Number of pages21
JournalJournal of Differential Equations
Volume263
Issue number10
DOIs
Publication statusPublished - 2017 Nov 15
Externally publishedYes

Keywords

  • Korman solution
  • Morse index
  • One-dimensional Liouville type equation
  • Positive solution
  • Symmetry-breaking bifurcation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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