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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (3): 55-63.doi: 10.6040/j.issn.1671-9352.0.2022.133

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一类奇异k-Hessian方程耦合系统的特征值问题

丁欢欢,何兴玥*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2023-03-02
  • 作者简介:丁欢欢(1997— ),女,硕士研究生,研究方向为常微分方程与动力系统. E-mail:hding_nwnu@163.com*通信作者简介:何兴玥(1995— ),女,博士研究生,研究方向为常微分方程与动力系统. E-mail:hett199527@163.com
  • 基金资助:
    国家自然科学基金资助项目(11961060);西北师范大学研究生科研资助项目(2021KYZZ01032)

Eigenvalue problem of a coupled system of singular k-Hessian equations

DING Huan-huan, HE Xing-yue*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2023-03-02

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摘要： 考察一类奇异k-Hessian方程耦合系统特征值问题径向解的存在性。通过构造适当的上下解,并利用Schauder不动点定理,证得该问题至少存在一个径向解,并获得该径向解的一些渐近性质。

关键词: k-Hessian方程, Hessian矩阵, 上下解, 奇异性

Abstract: This paper focuses on the existence of radial solutions for the eigenvalue problem of a coupled system of singular k-Hessian equations. By constructing the suitable upper and lower solutions and using the Schauder fixed point theorem, it is proved that at least one radial solution exists in this problem and some asymptotic properties of the radial solution are obtained.

Key words: k-Hessian equation, Hessian matrix, upper and lower solution, singularity

中图分类号: 

  • O175.8
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