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

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