Let \Omega \subsetR^N be a bounded smooth domain. We investigate the
effect of the mean curvature of the boundary \partial \Omega on the behaviour of the
solution to the homogeneous Dirichlet boundary value problem for the equation
\Delta u + f(u) = 0. Under appropriate growth conditions on f(t) as t approaches
zero, we find asymptotic expansions up to the second order of the solution in
terms of the distance from x to the boundary \partial \Omega
