| Summary: | We study the asymptotic behavior of radially symmetric solutions
to the subcritical semilinear elliptic problem
$$\displaylines{
-\Delta u = u^{\frac{N+2}{N-2}}/[\log(e+u)]^{\alpha}\quad \text{in }
\Omega=B_R(0)\subset\mathbb{R}^N,\cr
u>0,\quad \text{in } \Omega,\cr
u=0,\quad \text{on } \partial \Omega,
}$$
as $\alpha\to 0^+$.
Using asymptotic estimates, we prove that there exists an explicitly defined constant
L(N,R)>0, only depending on N and R, such that
$$
\limsup_{\alpha\to0^+} \frac{\alpha u_\alpha (0)^2}
{[\log(e+u_\alpha (0))]^{1+\frac{\alpha(N+2)}{2}}}
\leq L(N,R)
\le 2^*\liminf_{\alpha\to0^+}\frac{\alpha u_\alpha (0)^2}
{[\log(e+u_\alpha (0))]^{\frac{\alpha(N-4)}2}}.
$$
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