  In this paper we study the equation $-\Delta
u+\rho^{-(\alpha+2)}h(\rho^{\alpha}u)=0$ in a smooth bounded domain $\Omega$
where $\rho(x)=\textrm{dist}\,(x,\partial \Omega)$, $\alpha>0$ and $h$ is a
non-decreasing function which satisfies Keller-Osserman condition. We introduce
a condition on $h$ which implies that the equation is subcritical, i.e. the
corresponding boundary value problem is well posed with respect to data given
by finite measures. Under additional assumptions on $h$ we show that this
condition is necessary as well as sufficient. We also discuss b.v. problems
with data given by positive unbounded measures. Our results extend results of
\cite{MV1} treating equations of the form $-\Delta u+\rho^\beta u^q=0$ with
$q>1$, $\beta>-2$.
