摘要
利用Banach空间锥理论、算子的指数理论、上下解理论研究了含有一致椭圆型算子的椭圆边值问题变号解的存在性,同时分别得到了一个正解和一个负解.特别当非线性项是奇函数时,该边值问题至少存在一个正解,一个负解和两个变号解.
By using the Banach space cone theory,the exponential theory of operators and the theory of upper and lower solutions,the existence of sign-changing solutions for elliptic boundary value problems with uniformly elliptic operators is obtained.At the same time,a positive solution and a negative solution are obtained respectively.Especially when the nonlinear term is Odd function,the problem has at least one positive solution of the boundary value of a negative solution and two sign-changing solutions.
作者
纪宏伟
孙经先
崔玉军
JI Hong-wei;SUN Jing-xian;CUI Yu-jun(Department of Mathematics and Science Education,Nantong Teachers College,Nantong 226010,China;Department of Mathematics and Statistics,Xuzhou Normal University,Xuzhou 221116,China;College of Information Science and Engineering,Shandong University of Science and Technology,Qingdao 266590,China)
出处
《数学的实践与认识》
北大核心
2020年第6期212-218,共7页
Mathematics in Practice and Theory
基金
江苏省高校青蓝工程基金(2018)。
关键词
一致椭圆型算子
边值问题
锥
不动点指数
变号解
uniformly elliptic operator
boundary value problem
cone
fixed point index
sign-changing
