A refined result on sign changing solutions for a critical elliptic problem

In this work, we consider sign changing solutions to the critical elliptic problem Delta u + vertical bar u vertical bar 4/N-2 u = 0 in Omega(epsilon) and u = 0 on partial derivative Omega(epsilon), where Omega(epsilon) := Omega - (boolean OR(m)(i=1) (a(i) + epsilon Omega(i))) for small parameter epsilon > 0 is a perforated domain, Omega and Omega(i) with 0 is an element of Omega(i) (for all(i) = 1; ... ; m) are bounded regular general domains without symmetry in R-N and a(i) are points in Omega for all i = 1, ... , m. As epsilon goes to zero, we construct by gluing method solutions with multiple blow up at each point a(i) for all i - 1, ... , m