Symmetry-breakingsf or semilinear elliptic equations on finite cylindrical domains

Song-Sun Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study the existence and multiplicity of asymmetric positive solutions of a semilinear elliptic equation on finite cylinders with mixed type boundary conditions. By using a Nehari-type variational method, we prove that the numbers of asymmetric positive solutions are increasing without bound when the lengths of cylinders are increasing. On the contrary, by using the blow up technique, we obtain an a priori bound for positive solutions and then prove that all positive solutions must be symmetric when the cylinders are short enough.

Original languageEnglish
Pages (from-to)803-811
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - 1 Jan 1993


  • Cylinders
  • Symmetry breaking

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