| 三阶非线性奇异边值问题正解存在性 |
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| 引用本文： | 董艳艳,杜增吉,许圣梅. 三阶非线性奇异边值问题正解存在性[J]. 数学的实践与认识, 2008, 38(18) |
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| 作者姓名： | 董艳艳 杜增吉 许圣梅 |
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| 作者单位： | 徐州师范大学,数学科学学院,江苏,徐州,221116 |
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| 基金项目： | 国家自然科学基金,江苏省教育厅青蓝工程项目,江苏省研究生创新工程培养项目,徐州师范大学校科研和教改项目 |
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| 摘 要： | 研究三阶奇异边值问题-x=f(t,x,x,′x)″,t∈(0,1),x(0)=x(′0)=x(′1)=0,其中f:(0,1)×(0,∞)×R×R→R连续,f在x=0,t=0与t=1处具有奇性.通过运用上下解方法和单调逼近理论,得到了该问题新的正解的存在性结果.
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| 关 键 词： | 上下解 三阶奇异边值问题 正解 存在性 |
Existence of Positive Solutions for a Third-Order Nonlinear Singular Boundary Value Problem |
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| DONG Yan-yan,DU Zeng-ji,XU Sheng-mei. Existence of Positive Solutions for a Third-Order Nonlinear Singular Boundary Value Problem[J]. Mathematics in Practice and Theory, 2008, 38(18) |
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| Authors: | DONG Yan-yan DU Zeng-ji XU Sheng-mei |
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| Abstract: | In this paper,we are concerned with the following third-order nonlinear singular boundray value problem-x′″=f(t,x,x′,x″),t∈(0,1),x(0)=x′(0)=x′(1)=0,where f:(0,1)×(0,∞)×R×R→R is continuous and the nonlinear term f can have singularities at x=0,t=0,and t=1.The new existence result of positive solutions is given by using upper and lower solutions and monotone iterative techniques. |
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| Keywords: | upper and lower solutions Third-order singular boundary value problem positive solutions Existence |
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