Symmetry and nonexistence of positive solutions for fully nonlinear nonlocal systems. (February 2022)

• Record Type: Journal Article
• Authors: Luo, Linfeng; Zhang, Zhengce
• Is Part Of: Applied mathematics letters. Volume 124(2022)
• Publication Date: 2022-02
• Subjects: Fully nonlinear nonlocal systems -- Narrow region principle -- Direct method of moving planes -- Radial symmetry -- Nonexistence; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107674
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this article, we consider the following system involving fully nonlinear nonlocal operators F α ( u ( x ) ) + a 1 ( x ) v ( x ) = f ( v ( x ) ), G β ( v ( x ) ) + a 2 ( 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 R N under the weaker condition on a i ( x ) ( i = 1, 2 ). Furthermore, we obtain the nonexistence of positive solutions for the system on the half space.