| 一类非线性四阶两点边值问题的可解性 |
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| 引用本文： | 杨成,施恂栋,陈海亮.一类非线性四阶两点边值问题的可解性[J].黑龙江科技学院学报,2010,20(4):312-314. |
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| 作者姓名： | 杨成 施恂栋 陈海亮 |
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| 作者单位： | 中国矿业大学,理学院,江苏,徐州,221008 |
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| 摘 要： | 为深入探讨四阶两点边值问题解的存在性，利用Leray—Shauder不动点定理考察了一类非线性项含有一阶、二阶与三阶导数的四阶两点边值问题的解和正解的存在性，构造适当的Banach空间且利用相应的积分方程，得到了解和正解存在的充分条件，从而改进和推广了已有结果。
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| 关 键 词： | 四阶常微分方程 两点边值问题 解和正解 解的存在性 |
Solvability of class of nonlinear fourth-order two-point boundary value problems |
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| YANG Cheng,SHI Xundong,CHEN Hailiang.Solvability of class of nonlinear fourth-order two-point boundary value problems[J].Journal of Heilongjiang Institute of Science and Technology,2010,20(4):312-314. |
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| Authors: | YANG Cheng SHI Xundong CHEN Hailiang |
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| Institution: | (College of Sciences, China University of Mining ＆ Technology, Xuzhou 221008, China) |
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| Abstract: | Aimed at a deeper investigation into the existence of solutions for fourth-order two-point boundary value problems, this paper considers the existence of solutions and positive solutions for a class of fourth-order two-point boundary value problems whose nonlinear term contains first, second, and third derivatives by using the Leray - Schauder fixed point theorem. By constructing suitable Banach space and corresponding integral equation, two sufficient conditions are obtained. Some known results are improved and extended. |
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| Keywords: | fourth-order ordinary differential equation two-point boundary value problem solution and positive solution existence of solution |
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