Two-scale convergence of elliptic spectral problems with indefinite density function in perforated domains

Spectral asymptotics of linear periodic elliptic operatorswith indefinite (sign-changing)density function is investigated in perforated domains with the two-scale convergencemethod. The limiting behavior of positive and negative eigencouples depends cruciallyon whether the average of the weight over the solid part is positive, negative or equalto zero. We prove concise homogenization results in all three cases