| 一类四阶两点边值问题正解的存在性 |
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| 引用本文： | 杨变霞,路艳琼,陈瑞鹏.一类四阶两点边值问题正解的存在性[J].纯粹数学与应用数学,2011,27(2):273-279. |
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| 作者姓名： | 杨变霞 路艳琼 陈瑞鹏 |
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| 作者单位： | 西北师范大学数学与信息科学学院; |
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| 摘 要： | 运用上下解方法及拓扑度理论讨论了非齐次边界条件下四阶两点边值问题u″″(t)=f(u(t)),t∈(0,1),u(0)=u″(0)=u″(1)=0,u(1)=λ,其中λ＞0为参数,f∈C(0,+∞),0,+∞)).在非线性项满足一定的增长条件下,获得了上述问题存在正解时λ的取值范围.
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| 关 键 词： | 正解 存在性 上下解方法 拓扑度 |
Existence of positive solutions for a fourth-order two-point boundary value problem |
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| YANG Bian-xia,LU Yan-qiong,CHEN Rui-peng.Existence of positive solutions for a fourth-order two-point boundary value problem[J].Pure and Applied Mathematics,2011,27(2):273-279. |
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| Authors: | YANG Bian-xia LU Yan-qiong CHEN Rui-peng |
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| Institution: | YANG Bian-xia,LU Yan-qiong,CHEN Rui-peng(College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China) |
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| Abstract: | In this paper,by using the lower and upper solutions method and the topological degree theory,we study the following fourth-order two-point boundary value problem u″″(t) = f(u(t)),t ∈(0,1),u(0) = u″(0) = u″(1) = 0,u(1) = λ with nonhomogeneous boundary condition,where λ > 0 is a parameter,f ∈ C(0,+∞),0,+∞)).Under certain growth conditions on f,we determine the intervals of λ in which the above problems exist positive solutions. |
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| Keywords: | positive solutions existence lower and upper solutions topological degree theory |
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