| 一类四阶非线性微分方程两点边值问题的正解 |
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| 引用本文： | 陆海霞,孙经先.一类四阶非线性微分方程两点边值问题的正解[J].数学的实践与认识,2014(8). |
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| 作者姓名： | 陆海霞 孙经先 |
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| 作者单位： | 宿迁学院教师教育系;江苏师范大学数学科学学院; |
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| 基金项目： | 国家自然科学基金(10971179);宿迁学院科研基金(2011KY10) |
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| 摘 要： | 应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得了一类四阶非线性常微分方程两点边值问题{-u(4)(t)t=f(t,u(t)),≤t≤1,u(0)=u′(0)=u′(1)=u′″(1)=0正解的存在性.
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| 关 键 词： | 非线性边值问题 正解 不动点指数 锥 |
Positive Solutions of Two-point Boundary value Problems for Fourth-order Nonlinear Differential Equation |
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| Abstract: | By applying the theory of fixed point index and the cone theory,the existence of positive solutions of two-point boundary value problems for the fourth-order nonlinear differential equation {-u(4)(t)t=f(t,u(t)),≤t≤1,u(0)=u′(0)=u′(1)=u′″(1)=0 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator. |
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| Keywords: | nonlinear boundary value problem positive solution Fixed point index Cone |
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