Sign-changing blow-up solutions for Hénon type elliptic equations with exponential nonlinearity

We study the existence of sign-changing solutions with multiple concentration to the following boundary value problem−Δu=ε2|x|2α(eu−e−u) in Ω,u=0 on ∂Ω, where α>0α>0, Ω is a smooth bounded domain in R2R2 containing the origin, ε>0ε>0 is a small parameter. In particular we prove that if α≠1α≠1 then a nodal solution exists with a number of mixed positive and negative blow-up points up to 4.