  In this work we study the homogenization problem for nonlinear elliptic
equations involving $p-$Laplacian type operators with sign changing weights. We
study the asymptotic behavior of variational eigenvalues, which consist on a
double sequence of eigenvalues. We show that the $k-$th positive eigenvalue
goes to infinity when the average of the weight is nonpositive, and converge to
the $k-$th variational eigenvalue of the limit problem when the average is
positive for any $k\ge 1$.
