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

Analogues of the well known in the theory of analytic functions Phragmén-Lindelöff 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|^–2u)=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,>1,-1>q0, n>/2.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 279–283, February, 1992.