%0 Journal Article
%T 一类分数阶薛定谔－泊松系统非平凡解的存在性<br>Existence of Nontrivial Solution for a Class of Fractional Schro¨dinger-Poisson System
%A 孟娟霞
%J Advances in Applied Mathematics
%P 1704-1712
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.124177
%X 本文研究一类具有变号权的分数阶薛定谔－泊松系统<img src=\"Edit_574a5d0b-b91d-4efc-9139-6bc8d2621dd2.png\" alt=\"\" />非平凡解的存在性, 其中<img src=\"Edit_11c5b562-1cb4-4499-953e-941f3157374a.png\" alt=\"\" /> ,  s, t∈(0, 1) 且 4s + 2t &gt; 3, a(x)∈C(R<sup>3</sup>) 变号且lim<sub>|x|→∞</sub> a(x) = a<sup>∞</sup> &lt; 0, <img src=\"Edit_b31db360-1a10-4e36-960e-b712ea8a0f0a.png\" alt=\"\" />. 应用山路引理, 本文得到该系统至少存在一个非平凡解.<br />
In this paper, we are concerned with the existence of nontrivial solution for a class of fractional Schro¨dinger-Poisson system: <img src=\"Edit_9b068d0b-97d9-4458-af87-27b9de048a0c.png\" alt=\"\" />where <img src=\"Edit_07eac06d-e75f-456b-844f-e26ac28bd1d6.png\" alt=\"\" />, s, t ∈ (0, 1) and 4s + 2t &gt; 3, a(x) ∈ C(R<sup>3</sup>) is a sign-changing function with <span>lim</span><sub>|x|→∞</sub><span> a(x) = a</span><sup>∞</sup><span> &lt; 0</span>, <img src=\"Edit_78110fa6-509b-4ee3-9e25-d6b324e44740.png\" alt=\"\" />. By using mountain pass theorem, we obtain that this system has at least one nontrivial solution.
%K 分数阶薛定谔－泊松系统，变号权，非平凡解<br>Fractional Schro¨dinger-Poisson System
%K Sign-Changing Weight
%K Nontrivial Solution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=64649