Asymptotic behaviour of solutions to semilinear elliptic equations in unbounded domains

The second order uniformly elliptic equations with lower-order terms is studied in unbounded domains having a various structure at infinity. The homogeneous Neumann boundary conditions are posed on a non-compact part of the boundary. We investigate the asymptotic behaviour of solutions at infinity. In particular, the localization effect for the support of solutions is studied. The conditions on the growth of solutions at infinity, which cannot be realized, are found.