Асимптотика решений двумерного уравнения Гаусса—Бибербаха—Радемахера с переменными коэффициентами во внешней области

We consider an asymptotic behavior at infinity of solutions of a semi-linear second order elliptic equation containing exponential nonlinear term. We establish that any solution in a circle’s exterior tends to a negative infinity with the same rate as the fundamental solution of respective linear homogeneous elliptic equation.