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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (2): 206-216.doi: 10.3969/j.issn.1005-3085.2018.02.007

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一类Kirchhoff型四阶椭圆方程的无穷多个变号解（英）

陈   晶,   韩国栋   

  1. 陕西师范大学数学与信息科学学院，西安  710062
  • 收稿日期:2016-03-04 接受日期:2016-07-29 出版日期:2018-04-15 发布日期:2018-06-15
  • 通讯作者: 韩国栋 E-mail address: gdhan@snnu.edu.cn
  • 基金资助:
    国家自然科学基金(11101253)；中央高校基础研究经费(GK201503016)；陕西省教育厅科学计划(14JK1461).

Infinitely Many Sign-changing Solutions for Some Fourth-order Elliptic Equations of Kirchhoff Type

CHEN Jing,   HAN Guo-dong   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
  • Received:2016-03-04 Accepted:2016-07-29 Online:2018-04-15 Published:2018-06-15
  • Contact: G. Han. E-mail address: gdhan@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11101253); the Fundamental Research Funds for the Central Universities (GK201503016); the Science Program of Education Department of Shaanxi Province (14JK1461).

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摘要： 四阶Kirchhoff型椭圆问题来源于工程实际中的悬索桥模型．本文应用下降流不变集方法研究了一类四阶Kirchhoff型椭圆边值问题，在非线性项是奇函数且无穷远处超二次的条件下，证明了关于变号解存在性与多重性的两个定理．主要结果及其证明方法均不同于文献中的结果．

关键词: 四阶Kirchhoff型椭圆边值问题, 变号解, 临界点

Abstract: In engineering practice, the fourth-order elliptic equation of Kirchhoff type derives from the model of the suspension bridge. In the paper, two theorems on the existence and multiplicity of sign-changing solutions for some fourth-order elliptic equations of Kirchhoff type are proved by using the descending flow invariant set method under the assumption that the nonlinear term is odd and superquadric at infinity. The main results and the proofs are different from those in literatures.

Key words: fourth-order elliptic boundary value problems of Kirchhoff type, sign-changing solutions, critical points

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