数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 63-68.

• 论文 • 上一篇    下一篇

$k $-Hessian方程径向解的存在性与多解性

梁载涛(),单雪梦()   

  1. 安徽理工大学数学与大数据学院 安徽淮南 232001
  • 收稿日期:2019-10-09 出版日期:2021-02-26 发布日期:2021-01-29
  • 作者简介:梁载涛, E-mail: liangzaitao@sina.cn|单雪梦, E-mail: austshuda@163.com
  • 基金资助:
    国家自然科学基金(11901004);安徽省自然科学基金(1908085QA02)

Multiplicity of Radial Solutions of $ k$-Hessian Equations

Zaitao Liang(),Xuemeng Shan()   

  1. School of Mathematics and Big Data, Anhui University of Science and Technology, Anhui Huainan 232001
  • Received:2019-10-09 Online:2021-02-26 Published:2021-01-29
  • Supported by:
    Supported by the NSFC(11901004);the NSF of Anhui Province(1908085QA02)

摘要:

该文主要研究了 $k $-Hessian方程的Dirichlet问题.利用Leggett-Williams不动点定理,得到了一些关于非平凡径向解的存在性与多解性结论.

关键词: 径向解, Dirichlet问题, k-Hessian方程, Leggett-Williams不动点定理

Abstract:

This paper concerns with a Dirichlet problem of the $ k$-Hessian equation. By using the Leggett-Williams fixed point theorem, we get some results on the existence of triple and arbitrarily many nontrivial radial solutions.

Key words: Radial solutions, Dirichlet problem, k-Hessian equations, Leggett-Williams fixed point theorem

中图分类号: 

  • O175.8