%0 Journal Article
%T 具有Hardy项的半线性椭圆方程正径向对称解的存在性<br>Existence of Positive Radial Symmetric Solutions for Semilinear Elliptic Equation with Hardy Exponent
%A 李时雨
%J Pure Mathematics
%P 336-345
%@ 2160-7605
%D 2021
%I Hans Publishing
%R 10.12677/PM.2021.113045
%X <div style=\"text-align:justify;\">
	本文主要研究了以下具有Dirichlet边界条件的椭圆方程在B<sub>R</sub>(0)中正径向对称解的存在性:<img src=\"Edit_e33bcc40-5c5a-46f2-bbde-98865a187bc2.png\" alt=\"\" />，u&gt;0。其中<img src=\"Edit_14c3be4e-0546-4b8f-98e3-001a92e5b896.png\" alt=\"\" />&nbsp;&nbsp;<img src=\"Edit_cd4550a0-14e3-49b2-b9ec-dd928060500c.png\" alt=\"\" /> 且2<sup>*</sup>(a,s)是临界指数。我们主要利用山路引理、Moser迭代和比较原理证明该方程正径向对称解的存在性。<br />
In this paper, we study the existence of positive radial symmetric solutions of <img src=\"Edit_2050ecaf-d643-4f2d-836f-8e52fa5f28ac.png\" alt=\"\" /> 
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<div style=\"text-align:justify;\">
	, u&gt;0 in B<sub>R</sub>(0) with Dirichlet boundary condition. Here, <img src=\"Edit_25e0da15-73c1-4556-b166-a080d2f4dd0f.png\" alt=\"\" /><img src=\"Edit_73f1ad35-a03c-454c-9b6c-bca09d93b341.png\" alt=\"\" /> and 2<sup>*</sup>(a,s) is a critical exponent. We mainly prove the existence of positive radial symmetric solution of the equation by using the mountain pass lemma, Moser iteration and comparison principle.
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%K Hardy-Sobolev临界指数，山路引理，Moser迭代，比较原理<br>Hardy-Sobolev Critical Exponent
%K Mountain Pass Lemma
%K Moser Iteration
%K Comparison Principle
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=41186