Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations
Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations
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DOI：
10.1016/j.aej.2021.02.023
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发表时间：
2021-08
影响因子：
6.8
通讯作者：
Guotao Wang;Xueyan Ren;Lihong Zhang;B. Ahmad
中科院分区：
文献类型：
--
作者：
Guotao Wang;Xueyan Ren;Lihong Zhang;B. Ahmad
在本文中，我们考虑两种具有分数拉普拉斯势和哈代势的非线性薛定谔方程（λ| x| s，0< λ⩽ λ*，λ* 是 Hardy-Sobolev 不等式的常数），它们代表 Hartree 和 Pekar-Choquard 型时间相关分数 Hardy-Schrödinger 方程的广义形式。应用移动平面的直接方法，我们获得了给定方程的驻波的径向对称性和单调性。
In this paper, we consider two kinds of nonlinear Schrödinger equations with the fractional Laplacian and Hardy potential (λ| x| s, 0< λ⩽ λ∗, λ∗ is a constant of the Hardy-Sobolev inequality), which represent the generalized form of Hartree and Pekar-Choquard type time dependent fractional Hardy-Schrödinger equations. Applying the direct method of moving planes, we obtain the radial symmetry and monotonicity of the standing waves for the given equations.