中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (2): 142-147.doi: 10.13471/j.cnki.acta.snus.2019.02.018

• 论文 • 上一篇    下一篇

一类分数阶基尔霍夫方程的无穷多解

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
  • 收稿日期:2018-06-11 出版日期:2019-03-25 发布日期:2019-03-25

Infinitely many solutions of a class of fractional Kirchhoff equation

ZHANG Shengui   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
  • Received:2018-06-11 Online:2019-03-25 Published:2019-03-25

摘要:

研究带有分数阶p(x)-拉普拉斯算子的基尔霍夫方程 Dirichlet 边值问题。当非线性项超线性增长时,利用临界点理论中的喷泉定理,得到了无穷多高能量解存在的充分条件。

关键词: 基尔霍夫方程, 分数阶微分方程;p(x)-拉普拉斯算子, 超线性, 临界点

Abstract:

Dirichlet boundary value problem for Kirchhoff equation with fractional p(x)-Laplacian operator is studied. When the nonlinear term is growing superlinearly, some sufficient conditions for the existence of infinitely many high energy solutions are obtained by using the fountain theorem in critical point theory.

Key words: Kirchhoff equation, fractional differential equation, p(x)-Laplacian operator, superlinear, critical point

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