On the prescribed scalar curvature problem in RN, local uniqueness and periodicity

We obtain a local uniqueness result for bubbling solutions of the prescribed scalar curvature problem in R-N. Such a result implies that some bubbling solutions preserve the symmetry from the scalar curvature K(y). In particular, we prove in this paper that if K(y) is periodic in y(1) with period 1 and has a local maximum at 0, then a bubbling solution whose blow-up set is {(jL, 0, ..., 0) : j = 0, +/- 1, +/- 2, ...} must be periodic in y(1) provided the positive integer L is large enough. (C) 2015 Elsevier Masson SAS. All rights reserved.