2m阶Dirichlet边值问题的多解(英文)  

Multiple Solutions to 2mth-order Dirichlet Boundary Value Problems

作　　者：崔亚琼[1] 康淑瑰[1] 

机构地区：[1]山西大同大学数学计算科学学院,大同山西037009

出　　处：《数学进展》2010年第1期111-116,共6页Advances in Mathematics（China）

基　　金：The NSFC(No.10771128);NSF of Shanxi Province(No.2006011002).

摘　　要：本文讨论了非线性2m阶Dirichlet边值问题多解的存在性.在非线性项满足一定条件时,通过有效地利用锥中的不动点指数理论和解的反对称延拓法,得到关于变号解的一些新的存在结果.确切地说,得到该2m阶边值问题至少存在两个正解,两个负解和多个变号解.In this paper, we consider the existence of multiple solutions to nonlinear 2ruthorder Dirichlet boundary value problems. Under some general conditions on nonlinearity, by applying fixed point index theory in cones and an anti-symmetrical extension method of solution effectively, we get some new existence results concerning sign-changing solution. More precisely, we obtain that there exist at least two positive solutions, two negative solutions and multiple sign-changing solutions, respectively.

关 键 词：2m阶边值问题 不动点指数 反对称延拓法 变号解 

分 类 号：O177[理学—数学]