Symmetry and nonexistence of positive solutions for fully nonlinear nonlocal systems

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 solution...

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Bibliographic Details
Published inApplied mathematics letters Vol. 124; p. 107674
Main Authors Luo, Linfeng, Zhang, Zhengce
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2022
Subjects
Direct method of moving planes
Fully nonlinear nonlocal systems
Narrow region principle
Nonexistence
Radial symmetry
Direct method of moving planes
Fully nonlinear nonlocal systems
Radial symmetry
Nonexistence
Narrow region principle
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Summary: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.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2021.107674