On classical solutions to the Hartree equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:485

Article

Phuong Le^1,2 

[1] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam

[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

关键词: Hartree equation;    Choquard equation;    Liouville theorem;    Uniqueness result;    Classical solution;   

DOI  :  10.1016/j.jmaa.2020.123859

来源: Elsevier

【 摘 要 】

This paper is concerned with positive classical solutions to the Hartree equation -Delta u = (1/vertical bar x vertical bar(n-alpha) * u(p)) u(p-1) in R-n. When n <= 2, we show that the equation has no positive solution. When n >= 3, we prove that the equation has no positive solution if p < n+alpha/n-2, we also classify all positive solutions to the equation in the critical case p = n+alpha/n-2. The main novelty of this paper is that we cover the full range 0 < alpha < n and -infinity < p <= n+alpha/n-2 in our results. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free