Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: The radial case II

Abstract.

Let B be the unit ball of $\mathbb{R}^N$, $N\geq 3$, and $a,f:\mathbb{R}\rightarrow \mathbb{R}$ be two smooth functions. For $\eps>0$ small, the equation¶¶$\Delta u+a(|x|)u=N(N-2)f(|x|)u^{\frac{N+2}{N-2}-\epsilon}\mbox{in }B,\mbox{ on }\partial B\qquad (1)$¶¶has a positive radially symmetrical solution $\ue$. We describe the asymptotic behaviour of (u _ε as $\epsilon\to 0$. We also recover existence results for the critical equation.