| 一维p-Laplacian方程多点边值问题迭代解的存在性 |
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| 引用本文： | 马德香,葛渭高.一维p-Laplacian方程多点边值问题迭代解的存在性[J].数学学报,2008,51(3):447-456. |
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| 作者姓名： | 马德香 葛渭高 |
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| 作者单位： | 华北电力大学数学系,北京理工大学应用数学系 北京 102206,北京 100081 |
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| 摘 要： | 运用Mawhin定理、上下解方法以及单调迭代技巧得到了下列具有p-Laplacian算子的多点边值问题{(φ_p(u′))′+f(t,u)=0,0≤t≤1,u(0)=0,u(1)=∑_(i=1)~(m-2)γ_iu(η_i)迭代解的存在性.进一步地,在允许f(t,u)变号的前提下,我们给出充分条件以保证解的非负性和非正性.
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| 关 键 词： | Mawhin定理 单调迭代 多点边值问题 |
| 收稿时间： | 2006-4-27 |
Existence and Iteration of Solutions for a Multi-point Boundary Value Problem with a p-Laplacian Operator |
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| Institution: | De Xiang MA Department of Mathematics,North China Electric Power University,Beijing 102206,P.R.China Wei Gao GE Department of Mathematics,Beijing Institute of Technology,Beijing 100081,P.R.China |
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| Abstract: | By employing Mawhin's continuation theorem,we obtain the existence of solutions and establish a corresponding iterative scheme for BVP, {(φ_p(u′))′+f(t,u) =0,0≤t≤1,u(0) = 0,u(1) =∑_(i=1)~(m-2)γ_iu(η_i). The upper and lower solutions method and monotone iterative technique are used.Fur- thermore,we impose sufficient conditions on f(t,u) which can guarantee the existence of nonnegative or nonpositive solutions even when f(t,u) is allowed to change sign. |
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| Keywords: | Mawhin's continuation theorem iteration boundary value problem |
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