Energy integral of a nonlinear traction problem in a singularly perturbed periodically perforated domain

In this paper, we consider a nonlinear traction problem for the Lam\'e equations in a periodically perforated domain obtained by making in $\mathbb{R}^n$ a periodic set of holes, each of them of size proportional to $\epsilon$. Under suitable assumptions, we know that there exists a family of solutions $\{u(\epsilon,\cdot)\}_{\epsilon\in]0,\epsilon_1[}$ with a prescribed limiting behavior when $\epsilon$ approaches $0$. Then we investigate the energy integral of $u(\epsilon,\cdot)$ as $\epsilon$ tends to $0$, and we prove that such integral can be continued real analytically for negative values of $\epsilon$.