  We study the uniqueness and expansion properties of the positive solution of
the logistic equation $\Delta u+au=b(x)f(u)$ in a smooth bounded domain
$\Omega$, subject to the singular boundary condition $u=+\infty$ on
$\partial\Omega$. The absorption term $f$ is a positive function satisfying the
Keller--Osserman condition and such that the mapping $f(u)/u$ is increasing on
$(0,+\infty)$. We assume that $b$ is non-negative, while the values of the real
parameter $a$ are related to an appropriate semilinear eigenvalue problem. Our
analysis is based on the Karamata regular variation theory.
