  Homogenization is studied for a nonlinear elliptic boundary-value problem
with a large nonlinear potential. More specifically we are interested in the
asymptotic behavior of a sequence of p-Laplacians of the form $$
-\text{div}(a(\frac{x}{\varepsilon})|Du_\varepsilon|^{p-2}Du_\varepsilon)
+\frac{1}{\varepsilon}V(\frac{x}{\varepsilon})|u_\varepsilon|^{p-2}u_\varepsilon=f.
$$ It is shown that, under a centring condition on the potential $V$, there
exists a two-scale homogenized system with solution $(u, u_1)$ such that the
sequence $u_\varepsilon$ of solutions converges weakly to $u$ in $W^{1,p}$ and
the gradients $D_x u_\varepsilon$ two-scale converges weakly to $D_x u+ D_y
u_1$ in $L^p$, respectively. We characterize the limit system explicitly by
means of two-scale convergence and a new convergence result.
