Liouville‐type theorems for stable solutions of the Hénon–Lane–Emden system
Abstract
Abstract We investigate the Hénon–Lane–Emden system defined by We begin by establishing a general Liouville‐type theorem for the subcritical case. Then, we prove that the Hénon–Lane–Emden conjecture is valid for solutions stable outside a compact set, provided that , or , or . Additional Liouville‐type theorems for the subcritical case are also obtained. Furthermore, we address the supercritical case. To our knowledge, these results constitute the first Liouville‐type theorems for this class of solutions in the Hénon–Lane–Emden system. As a by‐product, several existing results in the literature are refined.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Waves and Solitons
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN