Sign-changing blowing-up solutions for a non-homogeneous elliptic equation at the critical exponent

We consider the equation−Δu=|u|4n−2u+εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω inRn,n≥3,withf≥0,f= 0. We find sign-changing solutions with large energy.The basic cell in the construction is the sign-changing nodal solution tothe critical Yamabe problem−Δw=|w|4n−2w, w∈D1,2(Rn)recently constructed in del Pino et al. (J Differ Equ 251(9):2568–2597,2011).