| Banach空间半直线上非线性二阶微分方程组正解的存在性 |
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| 引用本文： | 张兴秋.Banach空间半直线上非线性二阶微分方程组正解的存在性[J].数学研究及应用,2011,31(4):587-604. |
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| 作者姓名： | 张兴秋 |
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| 作者单位： | 华中科技大学数学与统计学院, 湖北 武汉 430074; 聊城大学数学科学院, 山东 聊城 252059 |
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| 基金项目： | 国家自然科学基金(Grant No.10971179),中国博士后科学基金,山东省优秀中青年科学家奖励基金(Grant No.BS2010SF004),山东省高等学校科技计划(Grant No.J10LA53). |
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| 摘 要： | In this paper, the cone theory and MSnch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived.
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| 关 键 词： | systems of singular differential equations cone and ordering positive solutions Monch fixed point theorem measure of non-compactness. |
| 收稿时间： | 2009/11/23 0:00:00 |
| 修稿时间： | 2010/1/19 0:00:00 |
Existence of Positive Solutions for Systems of Nonlinear Second-Order Differential Equations on the Half Line in a Banach Space |
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| Xing Qiu ZHANG.Existence of Positive Solutions for Systems of Nonlinear Second-Order Differential Equations on the Half Line in a Banach Space[J].Journal of Mathematical Research with Applications,2011,31(4):587-604. |
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| Authors: | Xing Qiu ZHANG |
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| Institution: | School of Mathematics and Statistics, Huazhong University of Science and Technology, Hubei, 430074, P.R.China;School of Mathematics, Lisocheng University, Shandong, 252059, P.R.China |
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| Abstract: | In this paper, the cone theory and M\"onch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived. |
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| Keywords: | systems of singular differential equations cone and ordering positive solutions M\"onch fixed point theorem measure of non-compactness |
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