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| 多项式型Sturm-Liouville边值问题正解的存在性和唯一性 | |
| 引用本文： | 续丽伟,杨志林. 多项式型Sturm-Liouville边值问题正解的存在性和唯一性[J]. 青岛建筑工程学院学报, 2010, 0(3): 104-107,128 |
| 作者姓名： | 续丽伟 杨志林 |
| 作者单位： | 青岛理工大学理学院,青岛266033 |
| 摘 要： | 运用微分方程的上下解方法,研究了二阶非线性Sturm-Liouville边值问题-（p（x）u′）′＋q（x）u=f（x,u）α0u（0）-β0u′（0）=0α1u（1）＋β1u′（1）=0正解的存在性和唯一性,并证明了对满足一定条件的u,存在迭代序列一致收敛到边值问题的唯一解.所得的结果推广和改进了前人的一些结果. |
| 关 键 词： | 二阶非线性常微分方程 边值问题 正解 存在 唯一性 迭代收敛 |
Existence and Uniqueness of Positive Solutions for a Sturm-Liouville Boundary Value Problem of Polynomial Type |
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| XU Li-wei,YANG Zhi-lin. Existence and Uniqueness of Positive Solutions for a Sturm-Liouville Boundary Value Problem of Polynomial Type[J]. Journal of Qingdao Institute of Architecture and Engineering, 2010, 0(3): 104-107,128 | |
| Authors: | XU Li-wei YANG Zhi-lin |
| Affiliation: | (School of Science,Qingdao Technological University,Qingdao 266033,China) |
| Abstract: | This paper is devoted to the existence and uniqueness of positive solutions for the nonlinear Sturm-Liouville boundary value problem.-（p（x）u′）′＋q（x）u=f（x,u）α0u（0）-β0u′（0）=0α1u（1）＋β1u′（1）=0The author proves that for u satisfied conditions,there exists sequence of iterations uniform converges to the unique solution of the boundary value problem.The main tool used in the proofs is the method of lower solutions and super solutions.The results presented extend and improve some ones in the previous literature. |
| Keywords: | nonlinear second order ordinary differential equation boundary value problem positive solution existence uniqueness iterative convergence |
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