LIOUVILLE THEOREMS FOR FRACTIONAL HENON EQUATION AND SYSTEM ON Rn

被引：26
|
作者：
Dou, Jingbo [1 ]
Zhou, Huaiyu [1 ]
机构：
[1] Xian Univ Finance & Econ, Sch Stat, Xian 710100, Shaanxi, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Weighted Hardy-Littlewood-Sobolev inequality; Henon equation; Liouville type theorem; method of moving planes; HARDY-LITTLEWOOD-SOBOLEV; POSITIVE SOLUTIONS; INTEGRAL-EQUATIONS; CLASSIFICATION;
D O I：
10.3934/cpaa.2015.14.1915
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish some Liouville type theorems for positive solutions of fractional Henon equation and system in R-n. First, under some regularity conditions, we show that the above equation and system are equivalent to the some integral equation and system, respectively. Then, we prove Liouville type theorems via the method of moving planes in integral forms.
引用
收藏
页码：1915 / 1927
页数：13
相关论文
共 50 条
  • [21] Liouville-type theorems for a system of fractional Laplacian equations
    Yin, Rong
    Zhang, Jihui
    Shang, Xudong
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2022, 67 (11) : 2646 - 2675
  • [22] Liouville theorems of solutions to mixed order Henon-Hardy type system with exponential nonlinearity
    Dai, Wei
    Peng, Shaolong
    ADVANCED NONLINEAR STUDIES, 2024, 24 (02) : 335 - 358
  • [23] Blow up solutions for a Liouville equation with Henon term
    Deng, Shengbing
    Musso, Monica
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 129 : 320 - 342
  • [24] Some Liouville theorems for the fractional Laplacian
    Chen, Wenxiong
    D'Ambrosio, Lorenzo
    Li, Yan
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 : 370 - 381
  • [25] SYMMETRY AND LIOUVILLE THEOREM FOR FRACTIONAL LAPLACIAN EQUATION BOTH IN Rn AND R+n
    Li, Jing
    Guan, Xiaohong
    Wang, Yamin
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2017, 18 (12) : 2163 - 2176
  • [26] Liouville Theorems for Fractional Parabolic Equations
    Chen, Wenxiong
    Wu, Leyun
    ADVANCED NONLINEAR STUDIES, 2021, 21 (04) : 939 - 958
  • [27] PHRAGMEN LIOUVILLE-TYPE THEOREMS AND LIOUVILLE THEOREMS FOR A LINEAR PARABOLIC EQUATION
    GLAGOLEVA, RY
    MATHEMATICAL NOTES, 1985, 37 (1-2) : 67 - 70
  • [28] Liouville-type theorems for polyhannonic systems in RN
    Liu, Jiaqun
    Guo, Yuxia
    Zhang, Yajing
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 225 (02) : 685 - 709
  • [29] Liouville type theorems for Hardy-Henon equations with concave nonlinearities
    Dai, Wei
    Qin, Guolin
    MATHEMATISCHE NACHRICHTEN, 2020, 293 (06) : 1084 - 1093
  • [30] Existence for the Henon Equation Involving the Fractional Laplacian
    Chen, Xiaoli
    Zhu, Yu
    ADVANCED NONLINEAR STUDIES, 2014, 14 (02) : 339 - 352
12345