On the homogenization of semilinear elliptic operators in perforated domains

Abstract

A second-order semilinear elliptic equation whose lower term has power-like growth at infinity with respect to the unknown function is considered. It is proved that a sequence of its solutions in perforated domains converges to a solution in the non-perforated domain as the diameters of the holes converge to zero with a rate depending on the power exponent of the lower term.