  In this article we consider the question of the existence of positive
symmetric solutions to the problems of the following type $\Delta u=a\left(
\left\vert x\right\vert \right) h\left( u\right) +b\left( \left\vert
x\right\vert \right) g\left( u\right) $ for $x\in \mathbb{R}^{N}$, which are
called entire large solutions. Here $N\geq 3$, and we assume that $a$ and $b$
are nonnegative continuous spherically symmetric functions on $\mathbb{R}% ^{N}
$. We extend results previously obtained for special cases of $h$ and $% g $
and we will describe a real-world model in which such problems may arise.
