A Refined Approach for Non-Negative Entire Solutions of Δ u + up = 0 with Subcritical Sobolev Growth

Abstract

Let N≥2{N\geq 2} and 1<p<(N+2)/(N-2)+{1<p<(N+2)/(N-2)_{+}}. Consider the Lane–Emden equation Δ⁢u+up=0{\Delta u+u^{p}=0} in ℝN{\mathbb{R}^{N}} and recall the classical Liouville type theorem: if u is a non-negative classical solution of the Lane–Emden equation, then u≡0{u\equiv 0}.

Keywords

• lane–emden equation
• liouville theorem
• non-existence
• scalar curvature equation
• yamabe equation
• 35b08
• 35b53
• 35j60