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 δ , whereas the relative size of the holes is determined by a second positive parameter ε . 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 ( ε ,  δ ) is close to the degenerate value (0, 0) .