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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 solutionsbifurcating from the bubble of the critical Sobolev equation.

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