共查询到19条相似文献,搜索用时 31 毫秒
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曾六川 《数学物理学报(A辑)》2004,4(6):654-660
该文在Banach空间中证明了,带误差的Ishikawa迭代序列强收敛到Lipschitz连续的增生算子方程的唯一解.而且,也给Ishikawa迭代序列提供了一般的收敛率估计.利用该结果还推得,带误差的Ishikawa迭代序列也强收敛到Lipschitz连续的强增生算子方程的唯一解. 相似文献
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一类非线性算子障碍问题的Schwarz算法 总被引:5,自引:2,他引:3
本文对一类非线性算子的障碍问题提出了几个Schwarz算法,所得迭代序列为上解序列或下解序列,它们单调收敛于问题的准确解. 相似文献
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二阶三点边值问题解的存在性与唯一性 总被引:1,自引:0,他引:1
利用单调迭代方法,研究了反序上、下解条件下的二阶微分方程三点边值问题解的存在性与唯一性,分别得到解存在与唯一的充分条件,在满足解的唯一性的条件下,给出了求解的迭代序列及误差估计式. 相似文献
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本文研究了非扩张半群的变分不等式的不动点解的迭代算法.利用变分不等式与不动点问题的解的关系,结合粘性逼近方法,建立了非扩张半群的不动点的两步迭代格式,证明了该方法所得到的迭代序列在一定条件下的强收敛性,并收敛于某变分不等式的唯一解. 相似文献
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用MAOR迭代算法求解一类L-矩阵的隐线性互补问题.证明了由此算法产生的迭代序列的聚点是隐线性互补问题的解.并且当问题中的矩阵是M-矩阵时,算法产生的迭代序列单调收敛于隐互补问题的解. 相似文献
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Banach空间中不连续非线性Volterra型积分方程的唯一解 总被引:12,自引:0,他引:12
本文在一般序Banach空间中研究了不连续非线性Volterra型积分方程的唯一解.在非常弱的条件下证明了非线性Volterra型积分方程的唯一解可以由迭代序列的一致极限得到,并给出了逼近解的迭代序列的误差估计式,然后应用到一阶微分方程的初值问题,本质改进并推广了最近的一些结果. 相似文献
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本文引入并研究了Hilbert空间中的一类广义多值拟变分包含问题.借助预解算子技巧构造了一个新的两步迭代算法来逼近广义多值拟变分包含的解,并且证明了其解的存在性以及迭代算法生成的迭代序列的收敛性. 相似文献
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在一般Banach空间中研究了一类无穷区间上不连续非线性积分方程的唯一解.在非常弱的条件下证明了非线性积分方程的唯一解可以由迭代序列的一致极限得到,并给出了逼近解的迭代序列的误差估计式,然后应用到无穷区间一阶微分方程的终值问题,本质改进(将紧型条件删去)并推广了一些结果. 相似文献
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陆海霞 《纯粹数学与应用数学》2013,(2):125-131
利用拟上下解方法和混合单调迭代法,研究了Banach空间中含间断项的非线性Sturm-liouville问题解的存在唯一性,并给出逼近解迭代序列的误差估计. 相似文献
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Fangfei Li Mei JiaXiping Liu Chunling LiGaoshang Li 《Nonlinear Analysis: Theory, Methods & Applications》2008
This paper studies the existence and uniqueness of solutions of second-order three-point boundary value problems with lower and upper solutions in the reversed order, obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method, and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution. 相似文献
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Hideaki Iiduka 《Journal of Optimization Theory and Applications》2011,148(3):580-592
Many practical problems such as signal processing and network resource allocation are formulated as the monotone variational
inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms to solve these problems have been
proposed. This paper discusses a monotone variational inequality with variational inequality constraint over the fixed point
set of a nonexpansive mapping, which is called the triple-hierarchical constrained optimization problem, and presents an iterative
algorithm for solving it. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain
assumptions. 相似文献
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This article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order. The sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method, meantime, the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given. Some results of previous literature are extended and improved. A numerical example is also included to illustrate the effectiveness of the proposed results. 相似文献
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《Nonlinear Analysis: Real World Applications》2007,8(3):980-996
The purpose of this work is to investigate the uniqueness and existence of nonlocal initial problems for a system of nonlinear parabolic equations weakly coupled with ordinary differential equations. The system of equations is considered in bounded and unbounded spatial domains. The uniqueness of the classical solution is proved by means of comparison principles for differential inequalities. The existence of the unique solution is obtained via a monotone iterative method. Applications are given to some model problems in epidemiology and ecology. 相似文献
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运用Schauder不动点定理和上下解方法研究了一类分数阶p-Laplacian边值问题正解的存在性和唯一性,并给出了唯一解的迭代序列. 相似文献
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本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果 相似文献