广西师范大学学报（自然科学版） ›› 2025, Vol. 43 ›› Issue (3): 106-112.doi: 10.16088/j.issn.1001-6600.2024041206

• 数学与统计学 • 上一篇    下一篇

一类非线性p-Laplace方程正规化解的存在性

郭新新, 钟延生*   

  1. 福建师范大学数学与统计学院,福建福州 350117
  • 收稿日期:2024-04-12 修回日期:2024-05-20 出版日期:2025-05-05 发布日期:2025-05-14
  • 通讯作者: 钟延生(1981—),男,福建龙岩人, 福建师范大学教授,博士。E-mail: zys08@fjnu.edu.cn
  • 基金资助:
    国家自然科学基金(11671085);福建省自然科学基金(2024J01479)

Existence of Normalized Solutions for a Class of Nonlinear p-Laplace Equations

GUO Xinxin, ZHONG Yansheng*   

  1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou Fujian 350117, China
  • Received:2024-04-12 Revised:2024-05-20 Online:2025-05-05 Published:2025-05-14

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摘要： 本文研究一类带扰动项Schrdinger方程在质量超临界情况(即p+p2/N*)下正规化解的存在性。首先,构造适当的辅助函数,验证能量泛函在约束空间上具有山路几何结构;然后,证明当hW1,p充分小时能量泛函满足Palais-Smale紧性条件,由此得到具有正能量山路解的存在性.

关键词: p-Laplace方程, 山路引理, Palais-Smale条件, 正规化解, Pohozaev流形

Abstract: The existence of positive normalized solutions for a class of Schrdinger equations with a perturbation for the mass supercritical case (that is, p+p2/N*) is discussed. Firstly, by constructing an appropriate auxiliary function, it is proved that the energy functional possesses a mountain-pass geometrical structure on the constraint space. Then, the existence of a mountain pass solution with positive energy is established when hW1,p is sufficiently small.

Key words: p-Laplace equation, mountain-pass theorem, Palais-Smale condition, normalized solution, Pohozaev manifold

中图分类号:  O175.29

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