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
Banach空间半直线上非线性二阶微分方程组正解的存在性
Existence of Positive Solutions for Systems of Nonlinear Second-Order Differential Equations on the Half Line in a Banach Space
投稿时间:2009-11-23  最后修改时间:2010-01-19
DOI:10.3770/j.issn:1000-341X.2011.04.003
中文关键词:  奇异微分方程组  锥与半序  正解  M\"onch 不动点定理  非紧性测度.
英文关键词:systems of singular differential equations  cone and ordering  positive solutions  M\"onch fixed point theorem  measure of non-compactness.
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).
作者单位
张兴秋 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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中文摘要:
      利用锥理论和M\"onch不动点定理结合单调迭代技巧给出了Banach空间中半直线上奇异二阶微分方程组正解存在的充分条件,并给出解的迭代程序.
英文摘要:
      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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