| 一维奇异p-Laplacian方程多解的存在性 |
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| 引用本文： | 张晓燕,孙经先.一维奇异p-Laplacian方程多解的存在性[J].数学物理学报(A辑),2006,26(1):143-149. |
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| 作者姓名： | 张晓燕 孙经先 |
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| 作者单位： | 山东大学数学与系统科学学院，徐州师范大学数学系 济南 250100，徐州 221116 |
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| 基金项目： | 国家自然科学基金(10371066)，数学天元基金(10526029)资助 |
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| 摘 要： | 该文通过利用Leggett-Williams定理,建立了一维奇异p-Laplacian非线性边值问题(\varphi(u'))'+a(t)f(u)=0,\u'(0)=u(1)=0 (或者u(0)=u'(1)=0),其中\varphi(s)=|s|^{p-2}s, p>1三解的存在性定理,推广并丰富了以往文献的一些结论.
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| 关 键 词： | p-Laplacian算子 Leggett-Williams定理 锥 |
| 文章编号： | 1003-3998（2006）01-143-07 |
| 收稿时间： | 2003-12-03 |
| 修稿时间： | 2004-11-25 |
Existence of Multiple Solutions for the One-dimensional Singular p-Laplacian Equations |
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| Zhang Xiaoyan,Sun Jingxian.Existence of Multiple Solutions for the One-dimensional Singular p-Laplacian Equations[J].Acta Mathematica Scientia,2006,26(1):143-149. |
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| Authors: | Zhang Xiaoyan Sun Jingxian |
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| Institution: | 1.School of Mathematics and System Science, Shandong University, Jinan 250100; 2. Department of Mathematics Xuzhou Normal University, Xuzhou 221116 |
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| Abstract: | This paper deals with the existence of multiple solutions for the singularp-Laplacian nonlinear BVP (\varphi(u'))'+a(t)f(u)=0,\ u'(0)=u(1)=0 (or u(0)=u'(1)=0), where \varphi(s)=|s|^{p-2}s,\ p>1. Sufficient conditions are established for the multiplicity of solutions of this problem by using Leggett-Williams theorem.The results presented here generalize many known results |
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| Keywords: | p-Laplacian operator Leggett-Williams theorem Cone |
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