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=ε^2|x|^{2α}(e^u−e{−u}) in Ω,u=0 on ∂Ω, where α>0, Ω is a smooth bounded domain in R2 containing the origin, ε>0 is a small parameter. In particular we prove that if α≠1 then a nodal solution exists with a number of mixed positive and negative blow-up points up to 4.