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

Abstract

We consider the elliptic system−Δui=ui3+∑j=1j≠iq+1βijuiuj2inR4,i=1,…,q+1, when α:=βij and β:=βi(q+1)=β(q+1)j for any i,j=1,…,q. If β<0 and |β| is small enough we build solutions such that each component u1,…,uq blows-up at the vertices of q polygons placed in different great circles which are linked to each other, and the last component uq+1 looks like the radial positive solution of the single equation.