  We investigate the qualitative properties of solution to the Zaremba type
problem in unbounded domain for the non-divergence elliptic equation with
possible degeneration at infinity. The main result is Phragm\'en-Lindel\"of
type principle on growth/decay of a solution at infinity depending on both the
structure of the Neumann portion of the boundary and the "thickness" of its
Dirichlet portion. The result is formulated in terms of so-called $s$-capacity
of the Dirichlet portion of the boundary, while the Neumann boundary should
satisfy certain "admissibility" condition in the sequence of layers converging
to infinity.
