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Existence and Monotone Iteration of Positive Solutions for a Nonlocal Boundary Value Problem with Delay and p-Laplacian Operator[J]. Journal of South China Normal University (Natural Science Edition), 2013, 45(2). DOI: 10.6054/j.jscnun.2013.01.004
Citation: Existence and Monotone Iteration of Positive Solutions for a Nonlocal Boundary Value Problem with Delay and p-Laplacian Operator[J]. Journal of South China Normal University (Natural Science Edition), 2013, 45(2). DOI: 10.6054/j.jscnun.2013.01.004

Existence and Monotone Iteration of Positive Solutions for a Nonlocal Boundary Value Problem with Delay and p-Laplacian Operator

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  • Received Date: December 18, 2011
  • Revised Date: February 09, 2012
  • A class of nonlocal boundary value problem with p-Laplacian operator and delay is studied. By using monotone iterative technique without the assumption of the existence of lower and upper solutions, some sufficient conditions on the existence of positive solutions for this boundary value problem are obtained and corresponding iterative schemes which converge to the solutions are established.
  • [1] 李森林.,温立志, 泛函微分方程[M],湖南科学技术出版社,1987.
    [2] Daqing Jiang., Multiple positive solutions for boundary value problems of second-order delay differential equations[J], Applied Mathematics Letters, 2002,15(5):575-583.
    [3] Dingyong bai, Yuantong xu., Existence of positive solutions for boundary-value problems of second-order delay differential equations[J], Applied Mathematics Letters, 2005,18(6): 621-630.
    [4] Wang, Youyu., Wenxia Zhao.; Ge., Weigao., Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian [J],Journal of Mathematical Analysis and Applications, 2007,326(1) 641-654.
    [5] XiaoBao Shu., YuanTong Xu., Triple positive solutions for a class of boundary value problems of second-order functional differential equations, Nonlinear Anal. 2005,61(8) 1401–1411.
    [6] Dexiang Ma.,Zengji Du.,Weigao Ge,Existence and iteration of monotone positive solutions for multipoint boundary value problem with p-Laplacian operator [J],Journal of Computers &Mathematics and Applications, 2005,50 (5) 729-739.
    [7] Bo Sun.,Weigao Ge., Existence and iteration of positive solutions to a class of Sturm–Liouville
    -like p-Laplacian boundary value problems [J],Nonlinear Analysis, 2008,69 (4) 1454-1461.
    [8] Huihui Pang.,Meiqiang Feng.,Weigao Ge, Existence and monotone iteration of positive solutions for a three-point boundary value problem[J],Applied Mathematics Letters, 2008,21(7):656-661.
    [9] Weibing Wang., Jianhua Shen., Positive solutions to a multi-point boundary value problem with delay[J]. Applied Mathematics and Computation, 2007,188(1) :96-102 .
    [10]Bo Du, Xueping Hu, Weigao Ge: Positive solutions to a type of multi-point boundary value problem with delay and one-dimensional p-Laplacian[J]. Applied Mathematics and Computation 2009,208(2): 501-510.

    [1] 李森林.,温立志, 泛函微分方程[M],湖南科学技术出版社,1987.
    [2] Daqing Jiang., Multiple positive solutions for boundary value problems of second-order delay differential equations[J], Applied Mathematics Letters, 2002,15(5):575-583.
    [3] Dingyong bai, Yuantong xu., Existence of positive solutions for boundary-value problems of second-order delay differential equations[J], Applied Mathematics Letters, 2005,18(6): 621-630.
    [4] Wang, Youyu., Wenxia Zhao.; Ge., Weigao., Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian [J],Journal of Mathematical Analysis and Applications, 2007,326(1) 641-654.
    [5] XiaoBao Shu., YuanTong Xu., Triple positive solutions for a class of boundary value problems of second-order functional differential equations, Nonlinear Anal. 2005,61(8) 1401–1411.
    [6] Dexiang Ma.,Zengji Du.,Weigao Ge,Existence and iteration of monotone positive solutions for multipoint boundary value problem with p-Laplacian operator [J],Journal of Computers &Mathematics and Applications, 2005,50 (5) 729-739.
    [7] Bo Sun.,Weigao Ge., Existence and iteration of positive solutions to a class of Sturm–Liouville
    -like p-Laplacian boundary value problems [J],Nonlinear Analysis, 2008,69 (4) 1454-1461.
    [8] Huihui Pang.,Meiqiang Feng.,Weigao Ge, Existence and monotone iteration of positive solutions for a three-point boundary value problem[J],Applied Mathematics Letters, 2008,21(7):656-661.
    [9] Weibing Wang., Jianhua Shen., Positive solutions to a multi-point boundary value problem with delay[J]. Applied Mathematics and Computation, 2007,188(1) :96-102 .
    [10]Bo Du, Xueping Hu, Weigao Ge: Positive solutions to a type of multi-point boundary value problem with delay and one-dimensional p-Laplacian[J]. Applied Mathematics and Computation 2009,208(2): 501-510.

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