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数学与物理学

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
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  • 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

  网络出版日期: 2021-03-05

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

Received date: 2019-05-14

  Revised date: 2019-07-04

  Online published: 2021-03-05

摘要

主要讨论矩阵型强奇异偏微分方程

其中,0∈Ω是Rnn≥3)中具有光滑边界的有界开集,Mx)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Mx)≡I(单位矩阵),-μ < -2时,方程不存在慢速增长的C2(Ω\{0})解。

本文引用格式

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 . DOI: 10.7523/j.issn.2095-6134.2021.01.003

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.

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