  In this note we consider a semilinear elliptic equation in $B_R$ with the
nonlinear boundary condition, where $B_R$ is a ball of radius $R$. Under
certain conditions, we establish a sufficient condition on the non-existence of
solutions provided that $R$ is sufficiently large. The main argument is based
on applying the asymptotic analysis to the equation with respect to $R\gg1$.
