Some Liouville theorems for Hénon type elliptic equations ✩

We investigate here the nonlinear elliptic equations − u = |x|αeu and − u = |x|α|u|p−1u with α >−2, p >1 and N 2. In particular, we prove some Liouville type theorems for weak solutions with finite Morse index in the low dimensional Euclidean spaces or half spaces. © 2011 Elsevier Inc. All rights reserved.