Liouville Type Theorems for PDE and IE Systems Involving Fractional Laplacian on a Half Space

被引：43

作者：

Dai, Wei ^{[1
]}

Liu, Zhao ^{[2
]}

Lu, Guozhen ^{[3
]}

机构：

[1] Beihang Univ BUAA, Sch Math & Syst Sci, Beijing 100191, Peoples R China

[2] Jiangxi Sci & Technol Normal Univ, Sch Math & Comp Sci, Nanchang 330038, Jiangxi, Peoples R China

[3] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

POTENTIAL ANALYSIS | 2017年 / 46卷 / 03期

基金：

美国国家科学基金会;

关键词：

Liouville type theorem; Dirichlet problem; Half space; Method of moving planes in integral forms; Nonexistence; Rotational symmetry; The fractional Laplacian; SEMILINEAR ELLIPTIC-EQUATIONS; ASYMPTOTIC SYMMETRY; INTEGRAL-EQUATION; R-N; CLASSIFICATION; NONEXISTENCE; REGULARITY;

D O I：

10.1007/s11118-016-9594-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, let a be any real number between 0 and 2, we study the Dirichlet problem for semi- linear elliptic system involving the fractional Laplacian:... (- ) a/ 2u(x) = vq(x), x. Rn +, (- ) a/ 2v(x) = up(x), x. Rn +, u(x) = v(x) = 0, x/. Rn +. (1) We will first establish the equivalence between PDE problem (1) and the corresponding integral equation (IE) system (Lemma 2). Then we use the moving planes method in integral forms to establish our main theorem, a Liouville type theorem for the integral system (Theorem 3). Then we conclude the Liouville type theorem for the above differential system involving the fractional Laplacian (Corollary 4).

引用

页码：569 / 588

页数：20

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