Two-parameter homogenization for a nonlinear periodic Robin problem for the Poisson equation: a functional analytic approach

We consider a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δδ . The relative size of each periodic perforation is instead determined by a positive parameter ϵϵ . We prove the existence of a family of solutions which depends on ϵϵ and δδ and we analyze the behavior of such a family as (ϵ,δ)(ϵ,δ) tends to (0, 0) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.