一类Kirchhoff型四阶椭圆方程的无穷多个变号解（英文）  

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

作　　者：陈晶 韩国栋[1] CHEN Jing;HAN Guo-dong(School of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062)

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2018年第2期206-216,共11页Chinese Journal of Engineering Mathematics

基　　金：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)

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.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.

关 键 词：四阶Kirchhoff型椭圆边值问题 变号解 临界点 

分 类 号：O175.4[理学—数学]