| 李敏,吴行平,唐春雷.含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解*[J].数学年刊A辑,2022,43(3):263~282 |
| 含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解* |
| Multiple Positive Solutions for Kirchhoff-Type Problems with Steep Potential Well and Concave-Convex Nonlinearities |
| Received:January 25, 2021 Revised:March 01, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0018 |
| 中文关键词: Kirchhoff 型问题, 凹凸非线性项, 陡峭势阱, Nehari 流形 |
| 英文关键词:Kirchhoff type problems, Concave-Convex nonlinearities, Steep potential well, Nehari manifold |
| 基金项目:国家自然科学基金(No.11971393) |
| Author Name | Affiliation | | LI Min | School of Mathematics and Statistics, Southwest University, Chongqing 400715,China
College of Basic Education, Chongqing Industry & Trade Polytechnic,Chongqing 408000, China. | | WU Xingping | Corresponding author. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China. | | TANG Chunlei | School of Mathematics and Statistics, Southwest University, Chongqing 400715,China. |
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| 中文摘要: |
| 在这篇文章中, 作者研究涉及凹凸非线性项的Kirchhoff型问题-(a + b ∫R3|▽u|2dx) Δu + λV (x)u = μf(x)|u|q?2u + |u|p?2u, x ∈ R3,u ∈ H1(R3),其中a,b > 0 是常数, λ, μ > 0 是参数, 1 < q < 2, 4 < p < 6 且 V 是一个非负连续位势. 在f(x) 和 V 的合适条件下,此问题正解的存在性和集中性能够通过Nehari 流形和Ekeland 变分原理得到. |
| 英文摘要: |
| In this paper, the authors research the following Kirchhoff type problem involving concave-convex nonlinearities ? (a + b ZR3|▽u|2dx) Δu + λV (x)u = μf(x)|u|q?2u + |u|p?2u, x ∈ R3,u ∈ H1(R3),where a, b > 0 are constants, λ, μ > 0 are parameters, 1 < q < 2, 4 < p < 6 and V is a nonnegative continuous potential. Under some suitable assumptions on f(x) and V ,the existence and concentration of positive solutions to this problem are obtained by using Nehari manifold and Ekeland variational principle. |
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