Behavior at infinity of solutions of second-order nonlinear equations of a particular class

Let $\Omega$ be an arbitrary, possibly unbounded, open subset of $\mathbb R^n$, and let $L$ be an elliptic operator of the form
$$ L=\sum_{i,j=1}^n \frac\partial{\partial x_i} \biggl(a_{ij}(x)\frac\partial{\partial x_j}\biggr). $$
The behavior at infinity of the solutions of the equation $Lu=f(|u|)\operatorname{sign}u$ in $\Omega$ is studied, where $f$ is a measurable function. In particular, given certain conditions at infinity, the uniqueness theorem for the solution of the first boundary value problem is proved.