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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (6): 48-55.doi: 10.6040/j.issn.1671-9352.0.2019.785

• • 上一篇    

变指数基尔霍夫型分数阶方程解的存在性

张申贵   

  1. 西北民族大学数学与计算机科学学院, 甘肃 兰州 730030
  • 发布日期:2020-06-01
  • 作者简介:张申贵(1980— ),男,博士,副教授,研究方向为非线性泛函分析和偏微分方程. E-mail:zhangshengui315@163.com
  • 基金资助:
    中央高校基本科研业务专项经费资助项目(31920180041);西北民族大学引进人才科研资助项目(xbxmuyjrc201907)

Existence of solutions for fractional Kirchhoff-type equation with variable exponent

ZHANG Shen-gui   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Published:2020-06-01

摘要: 研究一类变指数基尔霍夫型分数阶方程狄利克雷边值问题。当非线性项在无穷远处p+-超线性增长时, 利用临界点理论、变分方法及分数阶变指数空间理论, 得到了此类问题无穷多个解存在的充分条件。

关键词: 基尔霍夫型方程, 分数阶方程, 变指数, 临界点

Abstract: This paper studies a class of Dirichlet boundary value problem for fractional Kirchhoff-type equation with variable exponent. When the nonlinear term is p+-superlinear at infinity, some sufficient condition for the existence of infinitely many solutions is established by employing the critical point theory, variational methods and the theory of fractional variable exponent space.

Key words: Kirchhoff-type equation, fractional equation, variable exponent, critical point

中图分类号: 

  • O175.8
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