POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM

被引：0

作者：

王朋燕 ^{[1
]}

王永忠 ^{[1
]}

机构：

[1] Department of Applied Mathematics, Northwestern Polytechnical University

来源：

Acta Mathematica Scientia | 2018年 / 03期

基金：

中国国家自然科学基金;

关键词：

Weighted fractional system; positive solution; radial symmetry; monotonicity; non-existence;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this article, we study positive solutions to the system{A;u（x） = C;PV∫;(a1（x-y）(u（x）-u（y）))/(|x-y|;)dy = f(u（x）, B;v（x） = C;PV ∫;(a2（x-y）(v（x）-v（y）)/(|x-y|;)dy = g(u（x）,v（x）).To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.

引用

页码：935 / 949

页数：15

共 4 条

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[2] Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy–Littlewood–Sobolev system of integral equations
Yutian Lei
Congming Li
Chao Ma
[J]. Calculus of Variations and Partial Differential Equations, 2012, 45 : 43 - 61
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