%0 Journal Article
%T 分数阶Kirchhoff-Schr&#214;dinger-Poisson系统解的存在性<br>Existence of Nontrivial Solution for a Class of  Fractional  Kirchhoff-Schr&#214;dinger-Poisson System
%A 张召翔
%J Advances in Applied Mathematics
%P 2191-2198
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/AAM.2024.135208
%X 本文研究如下分数阶Kirchhoff-Schr？dinger-Poisson系统<img src=\"Edit_e3873d1b-ce19-4b92-a0bb-0020ce418cc2.png\" alt=\"\" />,
非平凡解的存在性, 其中 a, b &gt; 0 ,<img src=\"Edit_90fb70c2-9b0c-43f5-b548-434a23d1fafe.png\" alt=\"\" />,&nbsp; s, t ∈ (0, 1) 且 4s + 2t &gt; 3, W (x) ∈ C(R<sup>3</sup>) 变号且 lim<sub>|x|→∞</sub> W (x) = W<sub>∞</sub> &lt; 0 , <img src=\"Edit_232c87e9-7011-4f98-a894-d00122f4c3ed.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 study the existence of nontrivial solution for fractional Kirchhoff- Schr<span>？</span>dinger-Poisson system:<img src=\"Edit_4fde5281-8932-4d55-ad44-ddd9fb11467e.png\" alt=\"\" />,
where a, b &gt; 0, <img src=\"Edit_1c7bf283-eddd-4018-926b-c34e0f60bbb4.png\" alt=\"\" /> , s, t ∈ (0, 1) and 4s + 2t &gt; 3, W (x) ∈ C(R<sup>3</sup>) is a sign-changing function with lim<sub>|x|→∞</sub><span>&nbsp;</span> W (x) = W<sub>∞</sub> &lt; 0, <img src=\"Edit_6e4ff66c-ab48-4900-8983-abce3f3974b8.png\" alt=\"\" />. By using mountain pass lemma, we obtain that this system has at least one nontrivial solution.
%K 分数阶Kirchhoff-Schr&#214
%K dinger-Poisson系统，变号权，变分法<br>Fractional Kirchhoff-Schr&#214
%K dinger-Poisson System
%K Sign-Changing Weight
%K Variation Methods
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=87816