  This note introduces a class of nonlinear Neumann problems on balls expanding
with the radii tending towards infinity. Performing singular perturbation
arguments, we establish the corresponding concentration phenomenon and refined
asymptotic expansions with the precise first two order terms. In doing so, we
obtain the nontrivial boundary structure of solutions with effects coming from
the nonlinear Neumann boundary condition and the boundary mean curvature varied
with expanding domains.
