| 奇数阶边值问题正解的存在性与多重性 |
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| 引用本文： | 王淑丽,刘进生,邹杰涛.奇数阶边值问题正解的存在性与多重性[J].数学的实践与认识,2007,37(6):132-141. |
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| 作者姓名： | 王淑丽 刘进生 邹杰涛 |
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| 作者单位： | 1. 太原理工大学数学系,太原,030024
2. 北方工业大学,理学院,北京,100041 |
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| 摘 要： | 利用锥拉伸锥压缩不动点定理,证明了在一定条件下,下列非线性奇数阶方程(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.单个和多个正解的存在性,其中λ>0,12<τ<1,q∈N.得到了λ的区间Λ,对一切λ∈Λ,该问题至少有一个正解,同样也得到了该问题至少有两个正解λ相应的区间.
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| 关 键 词： | 正解 边值问题 不动点定理 锥 |
| 修稿时间： | 2006年6月12日 |
Existence and Multiplicity of Positive Solutions for Odd order Boundary Value Problems |
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| WANG Shu-li,LIU Jin-sheng,ZOU Jie-tao.Existence and Multiplicity of Positive Solutions for Odd order Boundary Value Problems[J].Mathematics in Practice and Theory,2007,37(6):132-141. |
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| Authors: | WANG Shu-li LIU Jin-sheng ZOU Jie-tao |
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| Abstract: | By using Krasnosel′skii fixed point theorem and under suitable conditions,we present the existence of single and multiple positive solutions for the following boundary value problems:(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0t1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.where λ>0,12<τ<1,q∈N.We derive explicit interval of λ such that for any λ in the interval,the existence of single positive solutions for λ in appropriate interval is also discussed. |
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| Keywords: | positive solution boundary value problems fixed point theorem cone |
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