反序上下解条件下二阶多点边值问题
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摘要
利用反序上下解方法研究二阶多点边值问题,当算子F映序区间入序区间时,证明该算子不动点的存在性.引入增算子,给出单调迭代序列,证明了最大解和最小解的存在性,并运用压缩映像原理讨论解的唯一性.
In this paper,we discuss the second-order multiple-point boundary value problems with upper and lower solutions in the reversed order. We get the existence of the maximal solution and the minimal solution by introducing an increasing operator and giving a monotone iterative sequence. The uniqueness is proved by using the contraction mapping principle.
In this paper,we discuss the second-order multiple-point boundary value problems with upper and lower solutions in the reversed order. We get the existence of the maximal solution and the minimal solution by introducing an increasing operator and giving a monotone iterative sequence. The uniqueness is proved by using the contraction mapping principle.
引文
[1]李凤艳,石金传.一类非线性项含有导数的3阶边值问题的正解[J].江西师范大学学报(自然科学版),2016,40(4):349-353.
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[4]任磊,王文武.一类变系数微分代数方程的数值解[J].江西师范大学学报(自然科学版),2014,38(1):54-57.
[5]ZHAI C B. Positive solutions for semi-positonethree-point boundary value problems[J]. J Computational and Applied Mathematics,2009,228(1):279-286.
[6] WEI L,LIU Y X. Study on a kind of nonlinear neumann boundary value problems[J]. Mathematica Applicata,2015,28(1):99-109.
[7]朱雯雯,徐有基.带非线性边界条件的一阶微分方程多个正解的存在性[J].四川师范大学学报(自然科学版),2016,39(2):226-230.
[8]XU J,ZHAO W. The existence of positive solutions of m-point boundary value problems for one kind of third-order ordinary differential equations[J]. Mathematics in Practice and Theory,2013,20(43):254-260.
[9]王丽,刘永莉,李永军,等.二阶隐式微分方程周期边值问题的上下解与迭合度[J].高校应用数学学报,2013,28(3):329-334.
[10]李海艳,李军燕,李利玫.带有一阶导数的脉冲微分方程多点边值问题解的存在性[J].四川师范大学学报(自然科学版),2017,40(2):163-171.
[11]李海艳,王敏,李利玫.脉冲微分方程m-点边值问题的多重正解[J].四川师范大学学报(自然科学版),2017,40(4):457-463.
[12]WEI L,LIU Y X. Research on the existence of solution of generalized curvature boundary value problems[J]. Acta Math Scientia,2014,34(4):938-947.
[13]李海艳,郭宇恒,李利玫.带有脉冲的二阶多点微分方程的边值问题[J].中北大学学报(自然科学版),2017,38(4):425-432.
[14]魏君,蒋达清,祖力.一维p-Laplace二阶脉冲微分方程的奇异边值问题[J].应用数学学报,2013,36(3):414-430.
[15]许绍元.增算子的不动点定理及其应用[J].江西师范大学学报(自然科学版),2000,24(1):25-27.
[16]杨爱军,王河林.反序上下解条件下周期边值问题的唯一解[J].浙江工业大学学报,2013,41(6):690-694.
[17]ZHANG Q M,JIANG D Q. Upper and lower solutions method and a second order three-point singular boundary value problem[J]. Comput Math Appl,2008(56):1059-1070.
[18]郭大均,孙经先,刘兆理.非线性常微分方程泛函方法[M].济南:山东科学技术出版社,1995.
[2]李耀红,张晓燕. Banach空间中一类二阶非线性脉冲积分-微分方程边值问题解的存在性[J].应用数学,2011,24(1):112-119.
[3]YAO Q L. Positive solutions of nonlinear second-order periodic boundary value problems[J]. Applied Mathematics Letters,2006,20(5):583-590.
[4]任磊,王文武.一类变系数微分代数方程的数值解[J].江西师范大学学报(自然科学版),2014,38(1):54-57.
[5]ZHAI C B. Positive solutions for semi-positonethree-point boundary value problems[J]. J Computational and Applied Mathematics,2009,228(1):279-286.
[6] WEI L,LIU Y X. Study on a kind of nonlinear neumann boundary value problems[J]. Mathematica Applicata,2015,28(1):99-109.
[7]朱雯雯,徐有基.带非线性边界条件的一阶微分方程多个正解的存在性[J].四川师范大学学报(自然科学版),2016,39(2):226-230.
[8]XU J,ZHAO W. The existence of positive solutions of m-point boundary value problems for one kind of third-order ordinary differential equations[J]. Mathematics in Practice and Theory,2013,20(43):254-260.
[9]王丽,刘永莉,李永军,等.二阶隐式微分方程周期边值问题的上下解与迭合度[J].高校应用数学学报,2013,28(3):329-334.
[10]李海艳,李军燕,李利玫.带有一阶导数的脉冲微分方程多点边值问题解的存在性[J].四川师范大学学报(自然科学版),2017,40(2):163-171.
[11]李海艳,王敏,李利玫.脉冲微分方程m-点边值问题的多重正解[J].四川师范大学学报(自然科学版),2017,40(4):457-463.
[12]WEI L,LIU Y X. Research on the existence of solution of generalized curvature boundary value problems[J]. Acta Math Scientia,2014,34(4):938-947.
[13]李海艳,郭宇恒,李利玫.带有脉冲的二阶多点微分方程的边值问题[J].中北大学学报(自然科学版),2017,38(4):425-432.
[14]魏君,蒋达清,祖力.一维p-Laplace二阶脉冲微分方程的奇异边值问题[J].应用数学学报,2013,36(3):414-430.
[15]许绍元.增算子的不动点定理及其应用[J].江西师范大学学报(自然科学版),2000,24(1):25-27.
[16]杨爱军,王河林.反序上下解条件下周期边值问题的唯一解[J].浙江工业大学学报,2013,41(6):690-694.
[17]ZHANG Q M,JIANG D Q. Upper and lower solutions method and a second order three-point singular boundary value problem[J]. Comput Math Appl,2008(56):1059-1070.
[18]郭大均,孙经先,刘兆理.非线性常微分方程泛函方法[M].济南:山东科学技术出版社,1995.