Asymptotic behavior of integral functionals for a two-parameter singularly perturbed nonlinear traction problem

We consider a nonlinear traction boundary value problem for the Lamé equations in an unbounded periodically perforated domain. The edges lengths of the periodicity cell are proportional to a positive parameter d, whereas the relative size of the holes is determined by a second positive parameter e. Under suitable assumptions on the nonlinearity, there exists a family of solutions {𝑢(𝜀,𝛿,·)}(𝜀,𝛿)∈]0,𝜀'[×]0,𝛿'[. We analyze the asymptotic behavior of two integral functionals associated to such a family of solutions when the perturbation parameter pair (e, d) is close to the degenerate value (0, 0).