| 具偏差变元的n阶微分方程共轭边值问题的多解性 |
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| 引用本文： | 杨雯抒,翁佩萱.具偏差变元的n阶微分方程共轭边值问题的多解性[J].华南理工大学学报(自然科学版),2004,32(7):81-85. |
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| 作者姓名： | 杨雯抒 翁佩萱 |
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| 作者单位： | 嘉应学院,数学系,广东,梅州,514015;华南师范大学,数学系,广东,广州,510631 |
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| 基金项目： | 广东省自然科学基金资助项目 (0 114 71) |
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| 摘 要： | 研究一类具偏差变元的(k，n-k)共轭边值问题多个正解的存在性，通过把所研究问题转化为相应的全连续算子的不动点问题，利用锥上不动点指数原理和Green函数界的估计，得到了此边值问题存在至少2个正解的两组充分条件．所得结果是没有偏差变元情形下常微分方程边值问题结论的拓广．算例说明所得结果的可应用性．
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| 关 键 词： | n阶微分方程 共轭边值问题 锥上不动点指数定理 正解 |
| 文章编号： | 1000-565X(2004)07-0081-05 |
| 修稿时间： | 2003年12月10 |
Existence of Multiple Solutions to the Conjugate Boundary Value Problem of the n-th Order Differential Equation with Deviating Arguments |
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| Yang Wen-shu,Weng Pei-xuan.Existence of Multiple Solutions to the Conjugate Boundary Value Problem of the n-th Order Differential Equation with Deviating Arguments[J].Journal of South China University of Technology(Natural Science Edition),2004,32(7):81-85. |
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| Authors: | Yang Wen-shu Weng Pei-xuan |
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| Institution: | Yang Wen-shu1 Weng Pei-xuan2 |
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| Abstract: | The existence of multiple positive solutions to a class of (k,n-k) conjugate boundary value problem of the n-th order di fferential equation with deviating arguments is investigated.By a transform,the discussed problem is firstly changed into a fixed-point problem of a completely continuous operator,and by using the fixed-point index theorem in cones and the evaluation of Green functions,two group of sufficient conditions are then obtained to guarantee the existence of two positive solutions to the problem.The results are the extension of those of the corresponding boundary value problem for the ordinary differential equation without deviating argument.The applicability of the obtained theorems is proved by an examlpe at last. |
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| Keywords: | n-th order differential equation conjugate boundary value problem fixed-point index theorem positive solution |
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