Liouville type theorems for fractional elliptic problems

2020/04/27 by Anh Tuan Duong, Duong, Anh Tuan, Van Hoang Nguyen +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.12609

openalex publication_date 2020/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish Liouville type theorems for stable solutions on the whole space \mathbb R^N to the fractional elliptic equation (-Δ)^su=f(u) where the nonlinearity is nondecreasing and convex. We also obtain a classification of stable solutions to the fractional Lane-Emden system \begincases (-Δ)^s u = v^p in \mathbb R^N (-Δ)^s v = u^q in \mathbb R^N \endcases with p>1 and q>1. In our knowledge, this is the first classification result for stable solutions of the fractional Lane-Emden system in literature.

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