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We study the Dirichlet problem in half-space for the equation u +g(u)jruj2 =0 ; where g is continuous or has a power singularity (in the latter case positive solutions are considered). The results presented give necessary and sucient conditions for the existence of (pointwise or uniform) limit of the solution as y!1; where y denotes the spatial variable, orthog- onal to the hyperplane of boundary-value data. These conditions are given in terms of integral means of the boundary-value function.

On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations