数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 281-291.doi: 10.1016/S0252-9602(11)60228-2

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EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

苑成军1,2, 文香丹3, 蒋达清1   

  1. 1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;
    2. School of Mathematics and Computer, Harbin University, |Harbin 150086, China;
    3. Department of |Mathematics, Yanbian University, Yanji |133002, China
  • 收稿日期:2008-04-18 修回日期:2009-06-03 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    The work was supported by Scientific Research Fund of Heilongjiang Provincial Education Department (11544032) and the National Natural Science Foundation of China (10571021, 10701020)

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

 YUAN Cheng-Jun1,2, WEN Xiang-Dan3, JIANG Da-Qing1   

  1. 1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;
    2. School of Mathematics and Computer, Harbin University, |Harbin 150086, China;
    3. Department of |Mathematics, Yanbian University, Yanji |133002, China
  • Received:2008-04-18 Revised:2009-06-03 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    The work was supported by Scientific Research Fund of Heilongjiang Provincial Education Department (11544032) and the National Natural Science Foundation of China (10571021, 10701020)

摘要:

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equa-tions, and provide sufficient conditions for the existence and uniqueness of positive solu-tion to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.

关键词: Mixed monotone operator, fixed point theorem, boundary value problems, existence, uniqueness

Abstract:

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equa-tions, and provide sufficient conditions for the existence and uniqueness of positive solu-tion to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.

Key words: Mixed monotone operator, fixed point theorem, boundary value problems, existence, uniqueness

中图分类号: 

  • 34B15