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Local uniqueness and periodicity induced by concentration
Author(s) -
Guo Yuxia,
Peng Shuangjie,
Yan Shusen
Publication year - 2017
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12029
Subject(s) - uniqueness , mathematics , scalar (mathematics) , critical exponent , curvature , mathematical analysis , critical point (mathematics) , symmetry (geometry) , geometry , scaling
We consider poly‐harmonic equations with critical exponents. Under some conditions on the coefficient K ( y ) in the equations near its critical points, we prove the existence and local uniqueness of solutions with infinitely many bubbles. The local uniqueness result implies that some bubbling solutions preserve the symmetry of the scalar curvature K ( y ) . Moreover, we also show that the conditions imposed are optimal to obtain such results.