Some Liouville theorems for Hénon type elliptic equations
In this paper the authors investigate the nonlinear elliptic equations \(-\Delta u=|x|^{\alpha_{e}u}\) and \(-\Delta u=|x|^{\alpha}|u|^{p-1}u\) with \(\alpha>-2, \;p>1\) and \(N\geqslant2\). The main objective of this paper is to classify such weak solutions of both problems under consideration in \(\mathbb R^{N}\) that are stable outside a compact set or which have finite Morse index in the low dimensional Euclidean spaces or half spaces.
scientific article; zbMATH DE number 6012143