一类具有 -1 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

• •

一类具有 -1 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:2022-10-11 修回日期:2023-02-06 发布日期:2023-03-15

On 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:2022-10-11 Revised:2023-02-06 Published:2023-03-15
Contact: ^† E-mail addresses: zhangheng201@mails.ucas.ac.cn
Supported by:
^* National Science Foundation of China (Grants 11971027 and 12171497)

摘要/Abstract

摘要： 本文研究一类具有奇异增长的拟线性椭圆方程$-\Delta u-u \Delta\left(u^{2}\right)=a(x) u^{-1}$。对于一般的$a(x) \in L^{p}(\Omega), \quad p>2$,我们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

Abstract: This paper deals with quasilinear elliptic equations of singular growth like $-\Delta u-u \Delta\left(u^{2}\right)=a(x) u^{-1}$. We establish the existence of positive solutions for general $a(x) \in L^{p}(\Omega), \quad p>2$, where Ω is a bounded domain in R^N with N≥1.

Key words: Quasilinear singular equations, -1 power

中图分类号:

O175.29

张衡, 孙义静. 一类具有 -1 指数的拟线性奇异偏微分方程[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2023.006.

Zhang Heng, Sun Yijing. On a class of quasilinear equations with -1 powers^*[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2023.006.

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一类具有 -1 指数的拟线性奇异偏微分方程

On a class of quasilinear equations with -1 powers^*

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一类具有 -1 指数的拟线性奇异偏微分方程

On a class of quasilinear equations with -1 powers*

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On a class of quasilinear equations with -1 powers^*