  We look for nonconstant, positive, radially nondecreasing solutions of the
quasilinear equation $-\Delta_p u+u^{p-1}=f(u)$ with $p>2$, in the unit ball
$B$ of $\mathbb R^N$, subject to homogeneous Neumann boundary conditions. The
assumptions on the nonlinearity $f$ are very mild and allow it to be possibly
supercritical in the sense of Sobolev embeddings. The main tools used are the
truncation method and a mountain pass-type argument. In the pure power case,
i.e., $f(u)=u^{q-1}$, we detect the limit profile of the solutions of the
problems as $q\to\infty$.
