| 段 誉,孙 歆,廖家锋.RN中一类带Hardy-Sobolev临界指数项的Kirchhoff型问题的正解*[J].数学年刊A辑,2023,44(3):323~334 |
| RN中一类带Hardy-Sobolev临界指数项的Kirchhoff型问题的正解* |
| Positive Solutions to a Class of Kirchhoff-Type Problems with Hardy-Sobolev Critical Exponent in RN |
| Received:February 23, 2021 Revised:May 04, 2023 |
| DOI：10.16205/j.cnki.cama.2023.0023 |
| 中文关键词: Hardy-Sobolev临界指数, Kirchhoff型问题, 正解, 变分法 |
| 英文关键词:Hardy-Sobolev critical exponent, Kirchhoff-Type problem, Positive solution, Variational method |
| 基金项目:国家自然科学基金(No.11661021)和毕节市科学技术项目(No.[2023]28, No.[2023]52) |
| Author Name | Affiliation | | DUAN Yu | College of Science, Guizhou University of Engineering Science, Bijie 551700,Guizhou, China. | | SUN Xin | College of Science, Guizhou University of Engineering Science, Bijie 551700,Guizhou, China. | | LIAO Jiafeng | Corresponding author. College of Mathematics Education, China West Normal University, Nanchong 637002, Sichuan, China. |
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| 中文摘要: |
| 研究如下一类带Hardy-Sobolev临界指数的Kirchhoff型问题: 其中N ≥ 3, a, λ ≥ 0, b, m > 0, 0 ≤ s < 2, h ∈ L2*/2*-1 (RN )为非零非负函数.当λ = 0时, 利用分析技巧获得了问题可解性结果. 当λ > 0时, 利用变分方法获得该问题正解的存在性.特别地, 当0 < m < 2-s/N-2时, 获得了问题至少存在两个正解. |
| 英文摘要: |
| In this article, the following class of Kirchhoff-type problems with Hardy-Sobolev critical exponent is considered where N ≥ 3, a, λ ≥ 0, b, m > 0, 0 ≤ s < 2, h ∈ L2*/2*-1 (RN ) is nonzero and nonnegative.When λ = 0, some existence results are obtained by some analysis techniques. When λ > 0,by using the variational method, the existence of positive solutions is obtained. Particularly,when 0 < m < 2-s/N-2 , at least two positive solutions are obtained. |
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