Finite Morse index solutions of the Hénon Lane–Emden equation

Abstract

Abstract In this paper, we are concerned with Liouville-type theorems of the Hénon Lane–Emden triharmonic equations in whole space. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether positive or sign-changing). Our proof is based on a combination of the Pohozaev-type identity, monotonicity formula of solutions and a blowing down sequence.

Keywords

• Liouville-type theorem
• Stable or finite Morse index solutions
• Monotonicity formula
• Blowing down sequence