Eigenvalue homogenization problem with indefinite weights

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 $k\ge 1$.