On the Solution of a Second-Order Nonlinear Equation in the Exterior of a Compact Set

In this paper, we study the behavior of solutions of a semilinear elliptic equation in the exterior of a compact set as $|x|\to\infty$. Such equations were considered by many authors (for example, Kondrat'ev, Landis, Oleinik, Veron, etc.). In the present paper, we study the case in which in the equation contains lower terms. The coefficients of the lower terms are arbitrary bounded measurable functions. It is shown that the solutions of the equation tend to zero as $|x|\to\infty$.