Eigenvalue homogenization for quasilinear elliptic operators

In this work we study the homogenization problem for (nonlinear) eigenvalues of quasilinear elliptic operators. We prove convergence of the first and second eigenvalues and, in the case where the operator is independent of $\varepsilon$, convergence of the full (variational) spectrum together whit an explicit in $k$ and in $\varepsilon$ order of convergence.