| 带p-Laplacian算子的四阶四点边值问题迭代解的存在性 |
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| 引用本文： | 庞慧慧,田敏,葛渭高.带p-Laplacian算子的四阶四点边值问题迭代解的存在性[J].数学的实践与认识,2008,38(3):130-134. |
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| 作者姓名： | 庞慧慧 田敏 葛渭高 |
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| 作者单位： | 北京理工大学,理学院数学系,北京,100081 |
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| 摘 要： | 考虑带p-Laplacian算子的四阶四点边值问题(φp(x″(t)))″=f(t,x(t),x″(t)),t∈0,1],x(0)-αx′(0)=0,x(1)+βx′(1)=0,φp(x″(ξ))-γ(φp(x″(ξ)))′=0,φp(x″(η))+δ(φp(x″(η)))′=0,其中φp(s)=s p-2s,p>1;0<ξ,η<1;f∈C(0,1]×R2,R).通过建立上下解方法得到迭代解的存在性.
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| 关 键 词： | 上下解 四点边值问题 单调迭代 |
| 修稿时间： | 2007年4月3日 |
Existence and Iteration of Solutions for Four-point Boundary Value Problems with a p-Laplacian |
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| PANG Hui-hui,TIAN Min,GE Wei-gao.Existence and Iteration of Solutions for Four-point Boundary Value Problems with a p-Laplacian[J].Mathematics in Practice and Theory,2008,38(3):130-134. |
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| Authors: | PANG Hui-hui TIAN Min GE Wei-gao |
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| Abstract: | We are considered with the fourth-order four-point boundary value problem with a p-Laplacian{(φp(x″(t)))″=f(t,x(t),x″(t)),t∈,x(0)-αx′(0)=0,x(1)+βx′(1)=0,φp(x″(ξ))-γ(φp(x″(ξ)))′=0,φp(x″(η))+δ(φp(x″(η)))′=0,where φp(s)=|s|p-2s,p>1;0<ξ,η<1;f∈C(×R2,R).The existence results for fourth-order four-point boundary value problem via the lower and apper solution method is obtained. |
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| Keywords: | cower and upper solution four-point boundary value problem monotone iteration |
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