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

Abstract

In this paper we consider the non-variational system 0.1 $$\begin{cases}-\Delta{u_i}=\Sigma_{j=1}^k\;a_{ij}u_j^{\frac{N+2}{N-2}}\;\;\;\;{\rm{in}} & \mathbb{R}^N,\\u_i>0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{in}}&\mathbb{R}^N,\\u_i\in{D^{1,2}(\mathbb{R}^N)}, \end{cases}$$ and we give some sufficient conditions on thematrix (aij)i, j =1,...,k which ensure the existence of solutions bifurcating from the bubble of the critical Sobolev equation.