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 delta. The relative size of each periodic perforation is instead determined by a positive parameter epsilon. We prove the existence of a family of solutions which depends on epsilon and delta and we analyze the behavior of such a family as (epsilon,delta) tends to (0,0 ) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.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 δ. The relative size of each periodic perforation is instead determined by a positive parameter ϵ. We prove the existence of a family of solutions which depends on ϵ and δ and we analyze the behavior of such a family as (ϵ, δ) tends to (0, 0) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory