On stable solutions of the fractional Henon-Lane-Emden equation

2014/10/24 by Fazly, Mostafa, Wei, Juncheng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.6786

Abstract

We derive monotonicity formulae for solutions of the fractional Hénon-Lane-Emden equation (-Δ)^s u=|x|^a |u|^p-1 u in ℝⁿ, when 00 and p>1. Then, we apply these formulae to classify stable solutions of the above equation.

Related

• Classification of the stable solution to the fractional 2
• Liouville type theorems for solutions of the weighted fractional Lane-Emden system
• Liouville type theorems for fractional elliptic problems
• Liouville-type Theorems for Stable Solutions of the Hénon-Lane-Emden System
• Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents