数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1424-1432.

• 论文 • 上一篇    下一篇

一类带临界指标的非自治Kirchhoff型方程非平凡解的存在性

张鹏辉,韩志清*()   

  1. 大连理工大学数学科学学院 辽宁大连 116023
  • 收稿日期:2021-09-28 出版日期:2022-10-26 发布日期:2022-09-30
  • 通讯作者: 韩志清 E-mail:hanzhiq@dlut.edu.cn

Existence of Nontrivial Solutions for Non-autonomous Kirchhoff-type Equations with Critical Growth in $ {{\Bbb R}} ^{3} $

Penghui Zhang,Zhiqing Han*()   

  1. School of Mathematical Sciences, Dalian University of Technology, Liaoning Dalian 116023
  • Received:2021-09-28 Online:2022-10-26 Published:2022-09-30
  • Contact: Zhiqing Han E-mail:hanzhiq@dlut.edu.cn

摘要:

该文研究下列非自治Kirchhoff型方程 非平凡解的存在性. 其中, 位势V(x) 和K(x) 在无穷远处消失, λ是一个大于零的参数. 该文证明: 存在λ*>0, 当$ \lambda\geq\lambda^* $时, 上述方程至少有一个非平凡解uλ.

关键词: Kirchhoff型方程, 临界指标, 变分法

Abstract:

We are concerned with the following non-autonomous Kirchhoff type equation in $ {{\Bbb R}} ^{3} $ with vanishing potentials $ V(x), K(x) $ at infinity and a Sobolev critical term $ u^{5} $, where $ \lambda\geq 0 $ is a parameter. We prove that there exists $ \lambda^*>0 $ such that the equation has a nontrivial solution $ u_{\lambda} $ for all $ \lambda\geq\lambda^* $.

Key words: Kirchhoff type equation, Critical growth, Variational methods

中图分类号: 

  • O175.2