I am interested in positive ground state solutions of the following elliptic pde:

$-\Delta u(x) = u(x)^{p-\epsilon} $ in the unit ball $B$ in $ R^N$ with $ u=0$ on $ \partial B$. Here $ p:=\frac{N+2}{N-2}$ and $ \epsilon>0$ is small.

Question: what is the behaviour of $ u_\epsilon(r)$ as $ \epsilon \searrow 0$ for $ r$ near zero.

Thanks for the replies.