分数阶Hartree方程负解的对称性
Symmetry of Negative Solutions of Fractional Hartree Equations
摘要: 本文研究了分数阶Hartree型方程负解的对称性。我们采用的方法是移动平面法，首先我们对方程的解作Kelvin变换。然后，我们证明了无穷远处衰减性定理，移动平面可以由此起步。最后，通过狭窄区域定理，我们证明了方程的解具有径向对称性。
Abstract: In this paper, we study the symmetry of negative solutions of fractional Hartree type equations. The method we adopted was the moving plane method. First, we performed Kelvin transformation on the solution of the equation. Then, we prove the decay theorem at infinity, from which the moving plane can start. Finally, by the narrow region theorem, we prove that the solution of the equation has radial symmetry.
文章引用：叶方琪. 分数阶Hartree方程负解的对称性[J]. 应用数学进展, 2022, 11(3): 980-990. https://doi.org/10.12677/AAM.2022.113105

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