  In this paper we study semi-stable, radially symmetric and decreasing
solutions $u\in W^{1,p}(B_1)$ of $-\Delta_p u=g(u)$ in $B_1\setminus\{0\}$,
where $B_1$ is the unit ball of $\mathbb{R}^N$, $p>1$, $\Delta_p$ is the
$p-$Laplace operator and $g$ is a general locally Lipschitz function. We
establish sharp pointwise estimates for such solutions. As an application of
these results, we obtain optimal pointwise estimates for the extremal solution
and its derivatives (up to order three) of the equation $-\Delta_p u=\lambda
f(u)$, posed in $B_1$, with Dirichlet data $u|_{\partial B_1}=0$, where the
nonlinearity $f$ is an increasing $C^1$ function with $f(0)>0$ and
$\lim_{t\rightarrow+\infty}{\frac{f(t)}{t^{p-1}}}=+\infty.$
  In addition, we provide, for $N\geq p+4p/(p-1)$, a large family of
semi-stable radially symmetric and decreasing unbounded $W^{1,p}(B_1)$
solutions.
