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

We study the existence of sign-changing solutions with multiple concentration to the following boundary value problem -Delta u = epsilon(2)vertical bar x vertical bar(2 alpha) (e(u)-e(-u)) in Omega, u=0 on partial derivative Omega where alpha> 0, Omega is a smooth bounded domain in R-2 containing the origin, epsilon > 0 is a small parameter. In particular we prove that if a alpha not equal 1 then a nodal solution exists with a number of mixed positive and negative blow-up points up to 4. (C) 2015 Elsevier Inc. All rights reserved.