Solutions to the master equations governing fractional vortices

Chang Shou Lin, Gabriella Tarantello, Yisong Yang

Research output: Contribution to journalArticle

Abstract

By means of variational methods, in this paper, we establish sharp existence results for solutions of the master equations governing 'fractional multiple vortices.' In the doubly periodic situation, the conditions for existence are both necessary and sufficient and give the upper bounds for the vortex numbers in terms of the size of the periodic cell domain. In the planar situation, there is no restriction on the vortex numbers. In both situations, the solutions are uniquely determined by the prescribed locations and the local winding numbers of the vortices.

Original languageEnglish (US)
Pages (from-to)1437-1463
Number of pages27
JournalJournal of Differential Equations
Volume254
Issue number3
DOIs
StatePublished - Feb 1 2013

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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