一类具有-1幂指数的拟线性奇异偏微分方程

doi:10.7523/j.ucas.2023.006

中国科学院大学学报 ›› 2025, Vol. 42 ›› Issue (1): 13-19.DOI: 10.7523/j.ucas.2023.006

• 数学与物理学 • 上一篇

一类具有-1幂指数的拟线性奇异偏微分方程

张衡, 孙义静

中国科学院大学数学科学学院, 北京 100049

收稿日期:2022-11-11 修回日期:2023-02-06 发布日期:2023-03-15
通讯作者: 张衡,E-mail:zhangheng201@mails.ucas.ac.cn
基金资助:
National Science Foundation of China (11971027，12171497)

A class of quasilinear equations with -1 powers

ZHANG Heng, SUN Yijing

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2022-11-11 Revised:2023-02-06 Published:2023-03-15
Supported by:
National Science Foundation of China (11971027，12171497)

摘要/Abstract

摘要： 研究一类具有奇异增长的拟线性椭圆方程-Δu-uΔ(u²)=a(x)u^-1。对于一般的a(x)∈L^p(Ω)，p>2，证明了该方程正解的存在性，其中Ω为ℝ^N中的有界区域且N≥1。

关键词: 拟线性奇异方程, -1幂指数, 椭圆方程

Abstract: This paper deals with quasilinear elliptic equations of singular growth like -Δu-uΔ(u²)=a(x)u^-1. We establish the existence of positive solutions for general a(x)∈L^p(Ω),p>2， where Ω is a bounded domain in ℝ^N with N≥1.

Key words: quasilinear singular equation, -1 power, elliptic equation

中图分类号:

O175.29

张衡, 孙义静. 一类具有-1幂指数的拟线性奇异偏微分方程[J]. 中国科学院大学学报, 2025, 42(1): 13-19.

ZHANG Heng, SUN Yijing. A class of quasilinear equations with -1 powers[J]. Journal of University of Chinese Academy of Sciences, 2025, 42(1): 13-19.

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一类具有-1幂指数的拟线性奇异偏微分方程

A class of quasilinear equations with -1 powers

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