无穷区间上具有p-Laplacian算子边值问题的正解

研究了一类在无穷区间上具有p-Laplacian算子的边值问题的迭代正解.利用单调迭代方法得到问题的迭代正解存在性的充分条件,同时得到了解的相应迭代序列,最后给出例子证明所得结论.     

具有混合单调非线性项的四阶微分方程两点边值问题

讨论了一类具有混合单调非线性项的四阶微分方程两点边值问题,运用一类混合单调算子的不动点定理及"和型"非线性算子的不动点定理,结合单调迭代技巧和格林函数的性质,获得方程正解存在且唯一的充分条件,并构造两个迭代序列收敛于此唯一解.最后,给出具体的例子验证了定理的正确性.     

半直线上Riemann-Liouville型奇异分数阶微分方程边值问题的单调迭代方法

运用不动点定理和单调迭代方法研究半直线上Riemann-Liouville型奇异分数阶微分方程边值问题的正解的存在性.在没有上、下解存在的假设下建立了边值问题存在两个正解的结果,构造了逼近正解的迭代格式,该迭代格式便于应用.     

半直线上具有p-Laplacian算子的Sturm-Liouville型脉冲边值问题的单调迭代正解

利用单调迭代方法得到了半直线上具有p-Laplacian算子的脉冲微分方程边值问题单调迭代正解的存在性,同时也给出了解的相应迭代序列.     

无穷区间上具有p-Laplacian算子的脉冲多点边值问题单调迭代正解的存在性

利用单调迭代方法得到了无穷区间上具有p-Laplacian算子的脉冲微分方程多点边值问题单调迭代正解的存在性,同时也给出了解的相应迭代序列.     

一类2n阶次线性奇异边值问题的正解

利用单调迭代方法给出了一类2n阶次线性奇异常微分方程正解的存在性,得到C~(2n-2)[0,1]和C~(2n-1)[0,1]正解存在的充分必要条件,也得到正解的唯一性.     

一类四阶两点边值问题正解的存在性

本文应用锥上的不动点指数理论,研究四阶两点边值问题—个正解及多个正解的存在性,给出了此类问题有一个正解及多个正解存在的与其相应线性问题的第一个特征值有关的充分条件,该条件中所涉及的值是最优的.     

带变号系数的经典Gelfand模型的正解

考察了经典Gelfand模型的正解的存在与迭代,其中非线性项的系数允许在[0,1]中改变符号。利用单调迭代方法得到了一个正解存在定理,给出了相应的迭代程序和收敛速度。由于这个迭代程序是从零函数开始的,因此它是简单、可行并且有效的。     

带有积分边值条件的两项分数阶微分方程正解的存在性

主要研究一类带有积分边值条件的两项分数阶微分方程在不同条件下正解的存在性及存在唯一性.利用上下解理论与Schauder不动点定理相结合的方法,得到正解的存在性.利用Banach压缩映像原理,推出正解的存在唯一性.并给出两个例子来说明结果的应用性.     

分数阶p-Laplacian边值问题正解的存在唯一性

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.     

Existence and iteration of positive solutions for high-order fractional differential equations with integral conditions on a half-line

In this paper, existence and iteration of positive solutions for a class of high-order fractional differential equations with integral conditions on a half-line is investigated. By means of a monotone iterative technique, we obtain not only the existence of positive solutions for the problems, but also establish iterative schemes for approximating the solutions.     

无穷区间上具积分边值条件的二阶非线性奇异微分方程组正解存在性（英文）

By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.     

Positive solutions for multipoint boundary value problem of fractional differential equations

In this paper, we study the existence of positive solutions for a multi-point boundary value problem of nonlinear fractional differential equations. By applying a monotone iterative method, some existence results of positive solutions are obtained. In addition, an example is included to demonstrate the main result.     

二次四元数系统正定解的迭代法

二次四元数系统XAX?BX=P是离散型Lyapunov方程正定解反问题的推广形式.本文在四元数体上讨论它的正定解存在性及迭代求解方法.利用等价二次方程的系数矩阵的极大极小特征值,获得其正定解的存在区间,并针对系数矩阵的不同情况构建出三种收敛的迭代格式.同时根据每种迭代的特点,给出了迭代初始矩阵的选取方法.最后通过四元数矩阵复算子实现Matlab环境下求解.数值算例验证了所给方法的有效及可行性.     

Banach空间半直线上非线性二阶微分方程组正解的存在性

In this paper, the cone theory and MSnch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived.     

具有连续系数的竞争扩散方程组的周期解(英文)

本文讨论了一类变系数的竞争扩散方程组,其中系数关于空间和时间变元连续,而关于时间变元是周期的.通过构造上下解,运用单调迭代方法证明了带Neumann边界条件的竞争扩散方程组正周期解的存在性和唯一性.     

Positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian

In this paper, we investigate the existence of positive solutions for a classes of m-point boundary value problems with p-Laplacian. By applying a monotone iterative technique, some sufficient conditions for the existence of twin positive solutions are established.     

Strongly coupled elliptic systems and applications to Lotka–Volterra models with cross-diffusion

The aim of this paper is to investigate the existence and method of construction of solutions for a general class of strongly coupled elliptic systems by the method of upper and lower solutions and its associated monotone iterations. The existence problem is for nonquasimonotone functions arising in the system, while the monotone iterations require some mixed monotone property of these functions. Applications are given to three Lotka–Volterra model problems with cross-diffusion and self-diffusion which are some extensions of the classical competition, prey–predator, and cooperating ecological systems. The monotone iterative schemes lead to some true positive solutions of the competition system, and to quasisolutions of the prey–predator and cooperating systems. Also given are some sufficient conditions for the existence of a unique positive solution to each of the three model problems.