一类带有奇异位势的强奇性偏微分方程的正解的性质

doi:10.7523/j.issn.2095-6134.2021.01.003

中国科学院大学学报 ›› 2021, Vol. 38 ›› Issue (1): 23-28.DOI: 10.7523/j.issn.2095-6134.2021.01.003

一类带有奇异位势的强奇性偏微分方程的正解的性质

唐露, 双震, 孙义静

中国科学院大学数学科学学院, 北京 100049

收稿日期:2019-05-14 修回日期:2019-07-04 发布日期:2021-03-05
通讯作者: 唐露
基金资助:
国家自然科学基金（11971027）资助

The properties of positive solutions for strongly singular equations with singular potential

TANG Lu, SHUANG Zhen, SUN Yijing

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

Received:2019-05-14 Revised:2019-07-04 Published:2021-03-05

摘要/Abstract

摘要：

主要讨论矩阵型强奇异偏微分方程

其中，0∈Ω是Rⁿ（n≥3）中具有光滑边界的有界开集，M（x）是定义在Ω上的实对称矩阵，-3 < -p < -1，-n < -μ < 0。对上述方程解的有界性及逼近速度进行研究，得到如下结论：当-n < -μ < -1-n/2时，方程的H₀¹解是无界解；当M（x）≡I（单位矩阵），-μ < -2时，方程不存在慢速增长的C²（Ω\{0}）解。

关键词: 奇异位势, 强奇性, 实对称矩阵

Abstract:

We discuss the strongly singular equations of matrix-type,

where Ω is a smooth bounded domain in Rⁿ (n ≥ 3) containing the origin, M(x) is a real symmetric matrix on Ω, -3 < -p < -1, and -n < -μ < 0. We show that all H₀¹-solutions are unbounded when -n < -μ < -1-n/2 and there exists no solution of slow growth when M(x)≡I (identity matrix) and -μ<-2.

Key words: singular potential, strong singularity, real symmetric matrix

中图分类号:

175.29

唐露, 双震, 孙义静. 一类带有奇异位势的强奇性偏微分方程的正解的性质[J]. 中国科学院大学学报, 2021, 38(1): 23-28.

TANG Lu, SHUANG Zhen, SUN Yijing. The properties of positive solutions for strongly singular equations with singular potential[J]. Journal of University of Chinese Academy of Sciences, 2021, 38(1): 23-28.

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一类带有奇异位势的强奇性偏微分方程的正解的性质

The properties of positive solutions for strongly singular equations with singular potential

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[1]	双震, 孙义静. 一类具有强奇性的矩阵型偏微分方程的正解的存在性[J]. 中国科学院大学学报, 2019, 36(3): 311-319.
[2]	谭玉鑫, 孙义静. 具有强奇性的半线性椭圆方程[J]. 中国科学院大学学报, 2017, 34(6): 660-666.