| 非线性微分方程组边值问题多个正解的存在性 |
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| 引用本文： | 马田田,赵增勤.非线性微分方程组边值问题多个正解的存在性[J].工程数学学报,2009,26(6). |
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| 作者姓名： | 马田田 赵增勤 |
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| 作者单位： | 马田田(首都师范大学数学科学学院,北京,100048);赵增勤(曲阜师范大学数学科学学院,曲阜,273165) |
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| 基金项目： | 国家自然科学基金，山东省自然科学基金 |
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| 摘 要： | 本文考虑了张力桥稳定性问题的数学模型,对相应的非线性微分方程组边值问题正解的存在性问题进行了研究.通过构造特殊的锥,在不同区间上利用锥拉伸和锥压缩不动点定理,给出了一类复合型非线性微分方程组边值问题一个或多个正解的存在性,并且给出几个例子说明本文定理的应用,从而有助于对实际工程中张力桥的稳定性问题的研究.
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| 关 键 词： | 微分方程组 边值问题 正解 不动点定理 |
Existence of Multiple Positive Solutions of Boundary Value Problems for Systems of Nonlinear Differential Equations |
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| MA Tian-tian,ZHAO Zeng-qin.Existence of Multiple Positive Solutions of Boundary Value Problems for Systems of Nonlinear Differential Equations[J].Chinese Journal of Engineering Mathematics,2009,26(6). |
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| Authors: | MA Tian-tian ZHAO Zeng-qin |
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| Affiliation: | MA Tian-tian1,ZHAO Zeng-qin2(1-School of Mathematical Sciences,Capital Normal University,Beijing 100048,2-School of Mathematical Sciences,Qufu Normal University,Qufu 273165) |
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| Abstract: | In this paper,we concern the mathematical model relevant with the stability of suspension bridge,which is about the existence of positive solutions of boundary value problems for systems of nonlinear differential equations.By constructing a special cone and using the fixed point theorems of cone expansion and cone compression in different intervals,we give the existence and multiplicity of positive solutions to boundary value problems for a kind of coupled systems of nonlinear differential equations.Example... |
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| Keywords: | systems of differential equations boundary value problems positive solutions fixed point theorems |
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