  In this paper we propose some approaches for finding of pointwise estimates
of a solution of the Dirichlet boundary value problem $-\Delta u \pm |u|^{q-1}
u = 0 $, $|u|=k$ when $|x|=d<1$ and $|u|=0$ when $|x|=1$ where $x\in \Omega =
\{x| d<|x|<1\}$. Along with these we consider the same boundary conditions for
the Laplace equation and get appropriate estimates for this easier case. We
indicate some way what permit to find upper and lower estimates of a solution
with explicit constants in turns.
