Local uniqueness and periodicity induced by concentration
Yuxia Guo, Shuangjie Peng, Shusen Yan · Proceedings of the London Mathematical Society · 2017
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.