On the behavior of solutions of quasilinear elliptic equations of second order in unbounded domains

Abstract

Analogues of the well known in the theory of analytic functions Phragmen-Lindeloff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form div(|∇u|α−2∇u)=f(x, u), where the function f(x, u) is locally bounded in IRn+1,f(x, 0)=0,uf(x, u)⩾a¦u¦1+q,a>0,α>1,α-1>q⩾0, n>/2.