On weak solutions to a fractional Hardy-Henon equation, Part II: Existence

被引：0

作者：

Hasegawa, Shoichi ^{[1
]}

Ikoma, Norihisa ^{[2
]}

Kawakami, Tatsuki ^{[3
]}

机构：

[1] Waseda Univ, Sch Fundamental Sci & Engn, Dept Math, 3-4-1 Okubo,Shinjuku Ku, Tokyo 1698555, Japan

[2] Keio Univ, Fac Sci & Technol, Dept Math, 3-14-1 Hiyoshi,Kohoku Ku, Yokohama, Kanagawa 2238522, Japan

[3] Ryukoku Univ, Fac Adv Sci & Technol, Appl Math & Informat Course, 1-5 Yokotani,Seta Oe Cho, Otsu, Shiga 5202194, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 227卷

关键词：

Fractional Hardy-Henon equation; Stable solutions; Separation property; SEMILINEAR ELLIPTIC EQUATION; LIOUVILLE THEOREMS; POSITIVE SOLUTIONS; CRITICAL EXPONENT; RADIAL SOLUTIONS; STABLE-SOLUTIONS; PROPERTY; CLASSIFICATION; INEQUALITIES; STABILITY;

D O I：

10.1016/j.na.2022.113165

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper and Hasegawa et al. (2021) treat the existence and nonexistence of stable weak solutions to a fractional Hardy-Henon equation (-Delta)(s)u = |x|(l)|u|(p-1) u in R-N, where 0 < s < 1, l > -2s, p > 1, N >= 1 and N > 2s. In this paper, when p is critical or supercritical in the sense of the Joseph-Lundgren, we prove the existence of a family of positive radial stable solutions, which satisfies the separation property. We also show the multiple existence of the Joseph-Lundgren critical exponent for some l is an element of(0, infinity) and s is an element of (0, 1), and this property does not hold in the case s = 1. (c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：48

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