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. 
Francesca Gladiali, Massimo Grossi, Christophe Troestler
math.AP