数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1094-1101.

• 论文 • 上一篇    下一篇

一类带临界指数的非齐次Kirchhoff型问题第二个正解的存在性

吉蕾1, 廖家锋2   

  1. 1 晋中学院数理学院 山西晋中 030600;
    2 西华师范大学公共数学学院 四川南充 637002
  • 收稿日期:2018-08-29 修回日期:2018-11-22 出版日期:2019-10-26 发布日期:2019-11-08
  • 通讯作者: 廖家锋 E-mail:liaojiafeng@163.com
  • 作者简介:吉蕾,E-mail:jilei@jzxy.edu.cn
  • 基金资助:
    四川省教育厅自然科学重点资助科研项目(18ZA0471)、西华师范大学英才科研项目(17YC383)、西华师范大学基本科研项目(18B015)和西华师范大学创新团队项目(CXTD2018-8)

Existence of the Second Positive Solution for a Class of Nonhomogeneous Kirchhoff Type Problems with Critical Exponent

Ji Lei1, Liao Jiafeng2   

  1. 1 College of Mathematics and Science, Jingzhong University, Shanxi Jingzhong 030600;
    2 College of Mathematics Education, China West Normal University, Sichuan Nanchong 637002
  • Received:2018-08-29 Revised:2018-11-22 Online:2019-10-26 Published:2019-11-08
  • Supported by:
    Supported by the Scientific Research Fund of Sichuan Provincial Education Department (18ZA0471), the Meritocracy Research Funds of China West Normal University (17YC383), the Fundamental Research Funds of China West Normal University (18B015) and the Innovative Research Team of China West Normal University (CXTD2018-8)

摘要: 研究了一类带临界指数的非齐次Kirchhoff型方程

其中Ω ? R3是一个非空有界开集,a ≥ 0,bλ > 0为参量,fL6/5(Ω)是个非零非负函数.利用变分方法获得了该问题第二个正解,补充并完善了文献[3]和[5]的结果.

关键词: Kirchhoff型问题, 临界指数, 变分法, 正解

Abstract: The following nonhomogeneous Kirchhoff type equations with critical exponent

where Ω is a smooth bounded domain in R3, a, b, λ > 0 are parameters and fL6/5 (Ω) is nonzero and nonnegative, are considered. By the variational method, the second positive solution is obtained which completes and improves the resulsts of[3] and[5].

Key words: Kirchhoff equation, Critical exponent, Variational method, Positive solution

中图分类号: 

  • O177.25