| 带p-Laplacian算子四阶四点边值问题的正解 |
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| 引用本文： | 茹凯,倪黎,韦煜明.带p-Laplacian算子四阶四点边值问题的正解[J].河南科学,2013(4). |
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| 作者姓名： | 茹凯 倪黎 韦煜明 |
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| 作者单位： | 广西师范大学数学科学学院,广西桂林 541004 |
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| 摘 要： | 考虑带p-Laplacian算子的四阶四点边值问题φp(u(″t)))″=a(t)(ft,u(t),u(″t)),t∈0,1],b1u(0)-b2u′(0)=0,b3u(1)+b4u′(1)=0,c1φp(u″(ξ))-c2(φp(u(″ξ)))′=0,c3φp(u(″η))+c4(φp(u(″η)))′=0其中:φp(s)=│s│p-2s,p>1;0<ξ,η<1;bi,ci(i=1,2,3,4)>0,c1c4+c2c3+c1c3(η-ξ)>0;a(t)∈C(0,1],0,+∞)).通过Avery-Henderson不动点定理得到边值问题存在至少两个正解.
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| 关 键 词： | 边值问题 锥 不动点定理 正解 |
The Positive Solutions to Four-order Four-point Boundary Value Problems with p-Laplacian |
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| Abstract: | We consider the four-order four-point boundary value problem with p-Laplacian φp(u(″t)))″=a(t)(ft,u(t),u(″t)),t∈0,1],b1u(0)-b2u′(0)=0,b3u(1)+b4u′(1)=0,c1φp(u″(ξ))-c2(φp(u(″ξ)))′=0,c3φp(u(″η))+c4(φp(u(″η)))′=0 where:φp(s)=│s│p-2s,p>1;0<ξ,η<1;bi,ci(i=1,2,3,4)>0,c1c4+c2c3+c1c3(η-ξ)>0;a(t)∈C(0,1],0,+∞)). The existence of at least two positive solutions to the boundary value problem is obtained by the Avery-Henderson fixed point theorem. |
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| Keywords: | boundary value problem cone fixed point theorem positive solution |
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