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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (10): 40-48.doi: 10.6040/j.issn.1671-9352.0.2019.157

• • 上一篇    

一类N-Kirchhoff方程正解的存在性

陈林   

  1. 伊犁师范大学数学与统计学院, 新疆 伊宁 835000
  • 发布日期:2019-10-12
  • 作者简介:陈林(1978— ),男,博士,副教授,研究方向为偏微分方程及其应用. E-mail:clzj008@163.com
  • 基金资助:
    新疆维吾尔自治区自然科学基金面上项目(2017D01C420)

Existence of positive solution for a class of N-Kirchhoff type equation

CHEN Lin   

  1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2019-10-12

摘要: 研究一类非线性项依赖于解的梯度项的N-Kirchhoff型问题解的存在性。运用基于迭代技巧的变分方法证明了该问题至少具有一个正的弱解。

关键词: N-Kirchhoff方程, N-Kirchhoff问题, 梯度项, 山路定理, 迭代方法

Abstract: This paper studies the existence of positive solution for a class of N-Kirchhoff type problem whose nonlinearity depends on the gradient of the solution. Applying a variational method and an iterative technique, the analysis proves that the problem has at least one positive week solution.

Key words: N-Kirchhoff equation, N-Kirchhoff problem, gradient term, mountain pass theorem, iterative method

中图分类号: 

  • O175.2
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