| 一类p-Kirchhoff方程基态解的存在性与唯一性 |
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| 引用本文： | 王壮壮,曾小雨. 一类p-Kirchhoff方程基态解的存在性与唯一性[J]. 数学学报, 2019, 62(6): 879-888 |
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| 作者姓名： | 王壮壮 曾小雨 |
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| 作者单位： | 武汉理工大学理学院 武汉 430070 |
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| 基金项目： | 国家自然科学基金（11871387）；中央高校基本科研业务费专项基金（2019IB009，2019IVB084） |
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| 摘 要： | 对于下面p-Kirchhoff型泛函■我们证明了约束在流形■上全局极小点或山路型临界点的存在性与唯一性,且这些临界点是某个Gagliardo-Nirenberg不等式的最优化子,特别当p∈(1,2]时,它们在不计平移意义下是唯一的.我们扩展了已有文献中p=2的情形的相关结果.
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| 关 键 词： | L~p归一化临界点 p-Kirchhoff方程 唯一性 |
Existence and Uniqueness of Ground State Solutions for a Class of p-Kirchhoff Equations |
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| Zhuang Zhuang WANG,Xiao Yu ZENG. Existence and Uniqueness of Ground State Solutions for a Class of p-Kirchhoff Equations[J]. Acta Mathematica Sinica, 2019, 62(6): 879-888 |
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| Authors: | Zhuang Zhuang WANG Xiao Yu ZENG |
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| Affiliation: | School of Sciences, Wuhan University of Technology, Wuhan 430070, P. R. China |
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| Abstract: | For the following p-Kirchhoff type functionalwe prove the existence and uniqueness of global minimum or mountain pass type critical points on the Lp-normalized manifold Sc:={u∈W1,p(Rn):∫Rn|u|pdx=cp}. We show that these critical points indeed are optimizers of a certain Gagliardo-Nirenberg inequality. Especially, when p ∈ (1, 2], they are unique up to translations. We extend some known results for the case of p=2 in previous papers. |
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| Keywords: | Lp-normalized critical point p-Kirchhoff equation uniqueness |
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