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

Abstract

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.