数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1622-1633.

• 论文 • 上一篇    下一篇

一类分数阶p-Laplace方程基态解的存在性及其渐进行为

韩娅玲1,*(),向建林2()   

  1. 1 中南财经政法大学统计与数学学院 武汉 430073
    2 武汉理工大学数学系 武汉 430070
  • 收稿日期:2020-05-26 出版日期:2020-12-26 发布日期:2020-12-29
  • 通讯作者: 韩娅玲 E-mail:ccnumathhyl@163.com;jlxiang2@163.com
  • 作者简介:向建林, E-mail: jlxiang2@163.com
  • 基金资助:
    国家自然科学基金(61503415)

Existence and Asymptotic Behavior of Ground State for Fractional p-Laplacian Equations

Yaling Han1,*(),Jianlin Xiang2()   

  1. 1 School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073
    2 Department of Mathematics, Wuhan University of Technology, Wuhan 430070
  • Received:2020-05-26 Online:2020-12-26 Published:2020-12-29
  • Contact: Yaling Han E-mail:ccnumathhyl@163.com;jlxiang2@163.com
  • Supported by:
    the NSFC(61503415)

摘要:

该文主要考虑一类含调和位势且非线性项是Lp约束临界指数的分数阶p-Laplace方程基态解的存在性及其渐近行为.首先利用约束变分理论分析了非线性项参数β在不同情形下方程基态解的存在性, 而后利用能量估计的方法分析了当非线性项参数逼近临界情形时基态解的渐近行为.

关键词: 基态解, 分数阶p-Laplace方程, 能量估计

Abstract:

In this paper, existence and asymptotic behavior of a fractional p-Laplacian equation with biharmonic potential and critical nonlinear was considered. First, variational method is used to obtain the existence and nonexistence of ground state under different parameter β. Then, the technique of energy estimates was used to get the asymptotic properties of ground state as parameter β tends to critical case.

Key words: Ground states, Fractional p-Laplacian equations, Energy estimates

中图分类号: 

  • O175.2