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2n阶两点边值问题的多重非平凡解
引用本文:韦忠礼,庞常词.2n阶两点边值问题的多重非平凡解[J].数学学报,2007,50(2):347-356.
作者姓名:韦忠礼  庞常词
作者单位:[1]山东建筑大学理学院,济南250014 [2]山东大学数学与系统科学学院,济南250100
基金项目:山东省自然科学基金(Y2004A01),山东省教育厅资助项目(J05A07)
摘    要:本文主要研究2n阶两点边值问题的多重非平凡解的存在性.利用不动点指数理论和Leray-schauder度,在一般的非线性条件下,证明了2n阶两点边值问题至少有六个非平凡解的存在性.而且,如果非线性项是奇函数,则至少有八个非平凡解的存在.

关 键 词:不动点指数  Leray-Schauder度  2n阶两点边值问题
文章编号:0583-1431(2007)02-0347-10
收稿时间:2005-7-1
修稿时间:2005-07-01

Multiple Nontrivial Solutions for 2nth-Order Boundary Value Problem
Zhong Li WEI, Chang Ci PANG.Multiple Nontrivial Solutions for 2nth-Order Boundary Value Problem[J].Acta Mathematica Sinica,2007,50(2):347-356.
Authors:Zhong Li WEI  Chang Ci PANG
Institution:Zhong Li WEI Chang Ci PANG School of Science,Shandong Jianzhu University,Jinan 250014,P.R.China School of Mathematics & Systems Science,Shandong University,Jinan 250100,P.R.China
Abstract:In this paper,we study the existence and multiplicity of nontrivial solutions for the 2nth-order two-point boundary value problems.Making use of the theory of fixed point index in cone and Leray-Schauder degree,under general conditions on nonlinearity,we prove that there exist at least six different nontrivial solutions for the 2nth-order two-point boundary value problems.Furthermore,if the nonlinearity is odd,we obtain that there exist at least eight different nontrivial solutions.
Keywords:fixed point index  Leray-Schauder degree  2nth-order two-point boundary value problem  
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