Stable Solutions of a Class of Degenerate Elliptic Equations - Yin Lang; Hairong Liu (Axioms)
This paper deals with the second-order semi-linear degenerate elliptic equation <semantics>yuyy+buy+Δxu+|u|α−1u=0,(x,y)∈Rn×(0,∞)</semantics>, where <semantics>n≥1,α>1</semantics>. We establish a Liouville theorem of stable solution of the degenerate equation mentioned above by using the energy method. The classification results for stable solutions belonging to <semantics>C2</semantics> can be thought of as an analogue of the recent results of Farina for the Lane–Emden equation.