In this paper we study the equation $-��u+��^{-(��+2)}h(��^��u)=0$ in a smooth bounded domain $��$ where $��(x)=\textrm{dist}\,(x,\partial ��)$, $��>0$ 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 $-��u+��^��u^q=0$ with $q>1$, $��>-2$.

30 pages