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The nontrivial solutions for fractional Schrödinger–Poisson equations with magnetic fields and critical or supercritical growth
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2021-04-30 , DOI: 10.1016/j.aml.2021.107358 Lintao Liu , Haibo Chen
中文翻译:
具有磁场和临界或超临界增长的分数阶Schrödinger-Poisson方程的非平凡解
更新日期:2021-05-18
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2021-04-30 , DOI: 10.1016/j.aml.2021.107358 Lintao Liu , Haibo Chen
In this paper, we study the following fractional Schrödinger–Poisson equation with magnetic field where , , , , is the fractional magnetic Laplacian, is a positive continuous potential, is a smooth magnetic potential. We mainly prove that the above equation has a nontrivial solution for small and .
中文翻译:
具有磁场和临界或超临界增长的分数阶Schrödinger-Poisson方程的非平凡解
在本文中,我们研究带磁场的以下分数次Schrödinger-Poisson方程 在哪里 , , , , 是分数磁性拉普拉斯算子, 是一个持续的正潜力, 是平滑的磁势。我们主要证明上面的方程对于一个小问题有一个非平凡的解 和 。