一类分数阶薛定谔－泊松系统非平凡解的存在性
Existence of Nontrivial Solution for a Class of Fractional Schro¨dinger-Poisson System
DOI: 10.12677/AAM.2023.124177, PDF, HTML, 下载: 117  浏览: 168 
作者: 孟娟霞：兰州理工大学理学院，甘肃 兰州
关键词: 分数阶薛定谔－泊松系统；变号权；非平凡解；Fractional Schro¨dinger-Poisson System； Sign-Changing Weight； Nontrivial Solution
摘要: 本文研究一类具有变号权的分数阶薛定谔－泊松系统非平凡解的存在性, 其中 , s, t∈(0, 1) 且 4s + 2t > 3, a(x)∈C(R3) 变号且lim|x|→∞ a(x) = a∞ < 0, . 应用山路引理, 本文得到该系统至少存在一个非平凡解.
Abstract: In this paper, we are concerned with the existence of nontrivial solution for a class of fractional Schro¨dinger-Poisson system: where , s, t ∈ (0, 1) and 4s + 2t > 3, a(x) ∈ C(R3) is a sign-changing function with lim|x|→∞ a(x) = a∞ < 0, . By using mountain pass theorem, we obtain that this system has at least one nontrivial solution.
文章引用：孟娟霞. 一类分数阶薛定谔－泊松系统非平凡解的存在性[J]. 应用数学进展, 2023, 12(4): 1704-1712. https://doi.org/10.12677/AAM.2023.124177

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