TY - JOUR
T1 - Solutions to the master equations governing fractional vortices
AU - Lin, Chang Shou
AU - Tarantello, Gabriella
AU - Yang, Yisong
PY - 2013/2/1
Y1 - 2013/2/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jde.2012.10.023
DO - 10.1016/j.jde.2012.10.023
M3 - Article
AN - SCOPUS:84870378900
SN - 0022-0396
VL - 254
SP - 1437
EP - 1463
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 3
ER -