Symmetry-breakingsf or semilinear elliptic equations on finite cylindrical domains

Song-Sun Lin*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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
Volume117
Issue number3
DOIs
StatePublished - 1 Jan 1993

Keywords

  • Cylinders
  • Symmetry breaking

Fingerprint Dive into the research topics of 'Symmetry-breakingsf or semilinear elliptic equations on finite cylindrical domains'. Together they form a unique fingerprint.

  • Cite this