| 非线性Neumann问题正解的存在性 |
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| 引用本文： | 马如云,陈瑞鹏,李杰梅.非线性Neumann问题正解的存在性[J].数学学报,2013(3):289-300. |
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| 作者姓名： | 马如云 陈瑞鹏 李杰梅 |
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| 作者单位： | 西北师范大学数学与统计学院;兰州交通大学数理学院 |
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| 基金项目： | 国家自然科学基金资助项目(11061030);国家自然科学天元基金资助项目(11226132);高校基本科研业务费专项资金资助项目(212084) |
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| 摘 要： | 研究非线性Neumann问题(p(t)u′)′+q(t)u=f(t,u),t∈(0,1),u′(0)=u′(1)=0正解的存在性,其中p,q∈C0,1]满足p(t)>0,0*,t∈0,1],b*,t∈0,1],b*为线性问题(p(t)u′)′+bu=0,u′(0)=0,u(1)=0的第一特征值.运用拓扑度理论及Rabinowitz全局分歧定理为上述问题建立了正解的存在性结果.
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| 关 键 词： | 存在性 特征值 Neumann问题 分歧方法 正解 |
Existence of Positive Solutions of Nonlinear Neumann Problems |
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| Ru Yun MA College of Mathematics and Statistics,Northwest Normal University,Lanzhou,P.R.China Rui Peng CHEN Jie Mei LI.Existence of Positive Solutions of Nonlinear Neumann Problems[J].Acta Mathematica Sinica,2013(3):289-300. |
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| Authors: | Ru Yun MA College of Mathematics and Statistics Northwest Normal University Lanzhou PRChina Rui Peng CHEN Jie Mei LI |
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| Institution: | College of Mathematics and Statistics,Northwest Normal University, Lanzhou 730070,P.R.China School of Mathematics and Physics,Lanzhou Jiaotong University, Lanzhou 730070,P.R.China |
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| Abstract: | We are concerned with the existence of positive solutions of the nonlinear Neumann problem (p(t)u')' +q(t)u-f(t,u),t∈(0,1) u'(0)=u'(1)=0 where p,q∈C0,1]with p > 0,0 < q < b~* in0,1],b~* is the first eigenvalue of the Robin problem (p(t)u')' + bu = 0,u'(0) = 0,u(1) = 0. By applying the topological degree theory and global bifurcation techniques,we establish the existence results of positive solutions for above problem. |
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| Keywords: | existence eigenvalues Neumann problem bifurcation methods positive solutions |
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