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Liouville-type theorems for a system of fractional Laplacian equations
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2021-07-01 , DOI: 10.1080/17476933.2021.1945586 Rong Yin 1 , Jihui Zhang 2 , Xudong Shang 3
中文翻译:
分数拉普拉斯方程系统的刘维尔型定理
更新日期:2021-07-01
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2021-07-01 , DOI: 10.1080/17476933.2021.1945586 Rong Yin 1 , Jihui Zhang 2 , Xudong Shang 3
Affiliation
In the paper, we study the following system of partial differential equations (PDEs) involving fractional Laplacian operators (1) (1) under the boundary conditions , where , , and . In order to overcome the difficulty that there are no corresponding maximum principles for the operators and in , we employ the method of moving planes in integral forms to the system of integral equations which is equivalent to System (1). Then, we obtain some Liouville type theorems for a pair of solutions of System (1) under different assumptions.
中文翻译:
分数拉普拉斯方程系统的刘维尔型定理
在本文中,我们研究了以下涉及分数拉普拉斯算子的偏微分方程 (PDE) 系统(1)(1)边界条件下, 在哪里,,和. 为了克服算子没有对应的最大值原则的困难和在,我们采用积分形式的平面移动方法到积分方程组,相当于系统(1)。然后,我们得到一些关于一对解的刘维尔型定理系统(1)在不同的假设下。