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

We consider the elliptic system $-Δu_i = u_i^3+\sum\limits_{j=1\atop j\not=i}^{q+1}{ β_{ij}}u_i u_j^2\ \hbox{in}\ \mathbb R^4, \ i=1,\dots,q+1.$ when $α:=β_{ij}$ and $β:=β_{i(q+1)}=β_{(q+1)j}$ for any $i,j=1,\dots,q.$ If $β<0$ and $|β|$ is small enough we build solutions such that each component $u_{1},\dots,u_q$ 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.

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