POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM

作     者：Pengyan WANG Yongzhong WANG Department of Applied Mathematics Northwestern Polytechnical University 王朋燕;王永忠

作者机构：Department of Applied Mathematics Northwestern Polytechnical University 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2018年第38卷第3期

页      面：935-949页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(11771354) 

主　　题：Weighted fractional system positive solution radial symmetry monotonicity non-existence 

摘      要：In this article, we study positive solutions to the system{Aαu（x） = Cn,αPV∫Rn（a1（x-y）（u（x）-u（y）））/（｜x-y｜n＋α）dy = f（u（x）, Bβv（x） = Cn,βPV ∫Rn（a2（x-y）（v（x）-v（y））/（｜x-y｜n＋β）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.