涉及分数阶拉普拉斯算子的非线性薛定谔方程组的解
Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian.
作者信息
Qu Meng, Yang Liu
机构信息
School of Mathematics and Statistics, Anhui Normal University, Wuhu, P.R. China.
出版信息
J Inequal Appl. 2018;2018(1):297. doi: 10.1186/s13660-018-1874-9. Epub 2018 Oct 29.
In this paper, we consider the following nonlinear Schrödinger system involving the fractional Laplacian operator: where . When Ω is the unit ball or , we prove that the solutions are radially symmetric and decreasing. When Ω is the parabolic domain on , we prove that the solutions are increasing. Furthermore, if Ω is the , then we also derive the nonexistence of positive solutions to the system on the half-space. We assume that the nonlinear terms , and the solutions , satisfy some amenable conditions in different cases.
在本文中，我们考虑如下涉及分数阶拉普拉斯算子的非线性薛定谔系统：其中 。当Ω为单位球或 时，我们证明解是径向对称且递减的。当Ω为 上的抛物区域时，我们证明解是递增的。此外，如果Ω为 ，那么我们还能推导出该系统在半空间上不存在正解。我们假设非线性项 、 以及解 、 在不同情形下满足一些适当的条件。
Zotero 插件