%0 Journal Article
%T 具有 Stein-Weiss 卷积部分的临界椭圆型方程 的正解<br>Positive Solution for the Critical Elliptic Equation with Stein-Weiss Type Convolution Parts
%A 顾啸风
%J Advances in Applied Mathematics
%P 2110-2124
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/AAM.2024.135199
%X 本文研究了具有 Stein-Weiss 卷积部分的临界椭圆方程<img src=\"Edit_c5f6d35c-5045-48fe-8fb5-324f42d714e1.png\" alt=\"\" />, (1) 其中 α ≥ 0，N &gt; 4，0 &lt; μ &lt; N，0 &lt; 2α + μ &lt; 4，<img src=\"Edit_acfcb130-fc9e-498e-86c5-8c00a5637b2a.png\" alt=\"\" />且 ？ 是 R<sup>N</sup> 中包含原点的C<sup>1</sup> 开有界域。我们证明了当 &gt; 0 且 2 &lt; p &lt; 2？<sub>α,μ</sub>时，方程 (2) 存在一个正的基态解。<br />
In this paper, we investigate the following critical elliptic equation with Stein-Weiss type convolution parts <img src=\"Edit_726c0a23-72bc-43ff-81e2-c2088888e4cd.png\" alt=\"\" />,	(2) where α ≥ 0, N &gt; 4, 0 &lt; μ &lt; N, 0 &lt; 2α + μ &lt; 4, <img src=\"Edit_85aec62d-4780-4bf7-9260-6b0886bf3d85.png\" alt=\"\" />and ？ is a C<sup>1</sup> open bounded domain in R<sup>N</sup> that contains the origin. We show that when &gt; 0 and 2 &lt; p &lt; 2？<span style=\"font-size:10px;\"><sub>α,μ</sub></span> , problem (2) possesses a positive ground state solution.
%K 临界椭圆方程，Stein-Weiss 卷积项，Nehari 流形，基态解<br>Critical Elliptic Equation
%K Stein-Weiss Convolution Part
%K Nehari Manifold
%K Ground State Solution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=87689