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

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