Homogenization of multivalued monotone operators with variable growth exponent

We consider the Dirichlet problem for an elliptic multivalued maximal monotone operator \begin{document}$ {\mathcal A}_\varepsilon $\end{document} satisfying growth estimates of power type with a variable exponent. This exponent \begin{document}$ p_\varepsilon(x) $\end{document} and also the symbol of the operator \begin{document}$ {\mathcal A}_\varepsilon $\end{document} oscillate with a small period \begin{document}$ \varepsilon $\end{document} with respect to the space variable \begin{document}$ x $\end{document} . We prove a homogenization result for this problem.