A non-variational system involving the critical Sobolev exponent. The radial case

In this paper we consider the non-variational system $$\{\begin{array}{ll}-\mathrm{\Delta }{u}_i={\sum }_{j=1}^k{a}_{ij}{u}_j^{(N+2)\mathrm{/}(N-2)}& \text{in }{\mathbb{R}}^N,\\ u_i>0& \text{in }{\mathbb{R}}^N,\\ u_i\in D^{1,2}({\mathbb{R}}^N)\mathrm{.}\end{array}$$ and we give some sufficient conditions on the matrix $(a_{ij}{)}_{i,j=1,\dots ,k}$ which ensure the existence of solutions bifurcating from the bubble of the critical Sobolev equation.