具有井位势的非线性分阶SchrO¨dinger-Poisson 方程组的基态解的存在性和渐近性

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具有井位势的非线性分阶SchrO^¨dinger-Poisson 方程组的基态解的存在性和渐近性
Existence and Asymptotic Behavior of Ground State Solutions for Nonlinear Fractional SchrO^¨dinger-Poisson Systemswith Steep Potential Well

DOI: 10.12677/AAM.2021.105191, PDF, 下载: 284 浏览: 380
作者: 王亚军：云南师范大学数学学院，云南昆明
关键词: 分数阶SchrO^¨dinger-Poisson 方程组；Nehari流形；变分方法；Fractional SchrO^¨dinger-Poisson System； Nehari Manifold； Variational Method

摘要: 在本文中, 我们研究了如下分阶 SchrO^¨dinger-Poisson 方程组

其中(−∆)^α是阶数为α∈(0, 1)的分数阶Laplace算子，λ >是一个参数，

是分数阶临街指数. 在 V, f满足适当条件下, 利用变分方法我们证明了基态解存在性. 及当λ → +∞ 基态解的渐近行为.

Abstract: In this paper, we study the following fractional SchrO^¨dinger-Poisson system:

where (−∆)^α denotes the fractional Laplacian of order α∈(0, 1), λ > 0 is a parameter,

is the fractional critical exponent. Under appropriate assumptions on V and f , we prove the existence of ground state solutions using variational methods. Furthermore, we also study the asymptotic behavior of ground state solutions as λ→+∞.

文章引用：王亚军. 具有井位势的非线性分阶SchrO^¨dinger-Poisson 方程组的基态解的存在性和渐近性[J]. 应用数学进展, 2021, 10(5): 1804-1824. https://doi.org/10.12677/AAM.2021.105191

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