| 2m阶Dirichlet边值问题的多解(英文) |
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| 引用本文： | 崔亚琼,康淑瑰.2m阶Dirichlet边值问题的多解(英文)[J].数学进展,2010(1). |
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| 作者姓名： | 崔亚琼 康淑瑰 |
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| 作者单位： | 山西大同大学数学计算科学学院; |
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| 基金项目： | The NSFC(No.10771128); NSF of Shanxi Province(No.2006011002). |
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| 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.
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| 关 键 词： | 2m阶边值问题 不动点指数 反对称延拓法 变号解 |
Multiple Solutions to 2mth-order Dirichlet Boundary Value Problems |
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| CUI Yaqiong,KANG Shugui.Multiple Solutions to 2mth-order Dirichlet Boundary Value Problems[J].Advances in Mathematics,2010(1). |
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| Authors: | CUI Yaqiong KANG Shugui |
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| Institution: | CUI Yaqiong~*,KANG Shugui (School of Mathematics , Computer Science,Shanxi Datong University,Datong,Shanxi,037009,P.R.China) |
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| Abstract: | In this paper,we consider the existence of multiple solutions to nonlinear 2mthorder 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. |
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| Keywords: | 2mth-order boundary value problem fixed point index anti-symmetrical extension method sign-changing solution |
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