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Symmetry and nonexistence of positive solutions for fully nonlinear nonlocal systems
Applied Mathematics Letters ( IF 3.7 ) Pub Date : 2021-09-23 , DOI: 10.1016/j.aml.2021.107674
Linfeng Luo 1 , Zhengce Zhang 1
Affiliation  

In this article, we consider the following system involving fully nonlinear nonlocal operators Fα(u(x))+a1(x)v(x)=f(v(x)),Gβ(v(x))+a2(x)u(x)=g(u(x)).Compared to results in Zhang et al. (2020), we apply a narrow region principle and a direct method of moving planes to prove that all positive solutions are radially symmetric about some point in RN under the weaker condition on ai(x) (i=1,2). Furthermore, we obtain the nonexistence of positive solutions for the system on the half space.



中文翻译:

完全非线性非局部系统正解的对称性和不存在性

在本文中,我们考虑以下涉及完全非线性非局部算子的系统 Fα((X))+一种1(X)v(X)=F(v(X)),Gβ(v(X))+一种2(X)(X)=G((X)).与张等人的结果相比。(2020),我们应用窄域原理和移动平面的直接方法来证明所有正解都是关于某个点径向对称的电阻N 在较弱的条件下 一种一世(X) (一世=1,2)。此外,我们获得了系统在半空间上不存在正解。

更新日期:2021-10-06
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