2012/04/12 by Chang‐Shou Lin, Chang-Shou Lin, Lin, Chang-Shou +4
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons #hep-th #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.1204.2818
arxiv created 2012/04/12 · openalex publication_date 2012/04/12 · arxiv updated 2012/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.