Systems of elliptic PDEs on R^N

We consider the system of second-order elliptic equations with the
nonlinear term depending on the solution and its first-order derivatives
on whole R^N. In order to solve it, firstly, we investigate auxiliary
systems on large balls B_n. Then, by suitable estimates and the
so-called tail estimate technique we show the convergence of auxiliary
solutions to the solution of the initial problem.