Existence and Monotone Iteration of Positive Solutions for a Nonlocal Boundary Value Problem with Delay and p-Laplacian Operator
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摘要: 研究了一类具有时滞的p-Laplacian方程的非局部问题.利用单调迭代方法在未引入上下解的条件下得到了该边值问题正解存在的充分条件，并确立了收敛到该正解的迭代序列.
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关键词:
- 正解
Abstract: 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.-
Keywords:
- positive solution
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[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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