Some Liouville theorems for Hénon type elliptic equations

By Chao Wang, D. Ye. 2012

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Abstract We investigate here the nonlinear elliptic equations − Δ u = | x | α e u and − Δ u = | x | α | u | p − 1 u 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8746b25dfbe777f4d324d2ec565f403e4d7d7097