具有对数非线性项的 $p$-Laplacian Schrödinger-Poisson 方程规范化解的存在性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2207-2224.

具有对数非线性项的 $p$-Laplacian Schrödinger-Poisson 方程规范化解的存在性

李明雪, 陈春柳, 张家锋^*()

贵州民族大学数据科学与信息工程学院贵阳 550025

收稿日期:2025-06-24 修回日期:2026-01-23 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 张家锋 E-mail:jiafengzhang@163.com
基金资助:
国家自然科学基金(12461024);贵州省教育厅自然科学研究项目(QJJ2023012);贵州省教育厅自然科学研究项目(QJJ2023061);贵州省教育厅自然科学研究项目(QJJ2023062);贵州省科技基金(QKHJCMS[2025]218);贵州民族大学自然科学研究项目(GZMUZK[2022]YB06)

Existence of Normalized Solutions for the $p$-Laplacian Schrödinger-Poisson Equations with Logarithmic Nonlinearity

Mingxue Li, Chunliu Chen, Jiafeng Zhang^*()

School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025

Received:2025-06-24 Revised:2026-01-23 Online:2026-12-26 Published:2026-08-14
Contact: Jiafeng Zhang E-mail:jiafengzhang@163.com
Supported by:
NSFC(12461024);Natural Science Research Project of Department of Education of Guizhou Province(QJJ2023012);Natural Science Research Project of Department of Education of Guizhou Province(QJJ2023061);Natural Science Research Project of Department of Education of Guizhou Province(QJJ2023062);Science and Technology Fund Project of Guizhou Province(QKHJCMS[2025]218);Natural Science Research Project of Guizhou Minzu University(GZMUZK[2022]YB06)

摘要/Abstract

摘要：

该文研究了具有对数非线性项的 $p$-Laplacian Schrödinger-Poisson方程, 通过将对数项进行分解, 得到该问题的能量泛函是 $C^1$ 的, 利用 Ekeland 变分原理和截断技术, 得到在 $L^p$-质量次临界和 $L^p$-质量超临界两种情形下方程规范化解的存在性, 并且得到方程弱解的 $C^{1,\alpha}$ 局部正则性.

关键词: $p$-Laplacian 方程, 对数Schr?dinger方程, 规范化解, 变分方法

Abstract:

This paper study the $p$-Laplacian Schrödinger-Poisson equations with logarithmic nonlinearity. By decomposing the logarithmic term, it is shown that the energy functional for this problem is of class $C^1$. By the Ekeland variational principle and truncation techniques, the existence of normalized solutions for the equation is obtained in both the $L^p$-mass subcritical and $L^p$-mass supercritical cases, and $C^{1,\alpha}$ local regularity of weak solution is obtained.

Key words: $p$-Laplacian equation, logarithmic Schr?dinger equation, normalized solutions, variational method

中图分类号:

O177.91

李明雪, 陈春柳, 张家锋. 具有对数非线性项的 $p$-Laplacian Schrödinger-Poisson 方程规范化解的存在性[J]. 数学物理学报, 2026, 46(6): 2207-2224.

Mingxue Li, Chunliu Chen, Jiafeng Zhang. Existence of Normalized Solutions for the $p$-Laplacian Schrödinger-Poisson Equations with Logarithmic Nonlinearity[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2207-2224.

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