Segregated solutions for a critical elliptic system with a small interspecies repulsive force

We consider the elliptic system-Delta u(i) = u(i)(3)+ Sigma(q+1)(j=1 j not equal i) beta(ij)u(i)u(j)(2) in R-4, i = 1, ..., q + 1,when alpha := beta(ij) and beta := beta(i(q+1)) = beta((q+1)j) for any i, j = 1, ... , q. If beta < 0 and |beta| is small enough we build solutions such that each component u(1), . . . , u(q) blows-up at the vertices of q polygons placed in different great circles which are linked to each other, and the last component u(q+1) looks like the radial positive solution of the single equation. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org /licenses/by-nc-nd /4 .0/).