二阶非线性q-差分微分方程两点边值问题两个迭代正解的存在性*

研究了二阶非线性q-差分微分方程两点边值问题,给出了系统两个正解存在的充分条件. 与其他文献中使用的不动点定理不同,文章不仅证明了该系统正解的存在性, 而且还利用单调迭代技巧给出了逼近正解的迭代格式.     

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.     

Monotone iteration method for differential equations involving integral boundary conditions on the half line

By applying the monotone iterative methods, we obtain the existence of monotone positive solutions for integral boundary value problems of differential equations on the half line, and establish the iterative schemes for approximating the solutions. Our approach is based on the fixed point theorem and the monotone iterative technique. The existence of lower and upper solutions is not needed.     

Necessary and sufficient condition for the existence of positive solutions of a coupled system for elastic beam equations

In this work, by using fixed point theorem and monotone iterative technique, the author establishes a necessary and sufficient condition of the existence of positive solutions for a class of nonlinear singular elastic beam differential system under reasonable conditions. Moreover, some uniqueness results of positive solution and the estimate of convergent rate of the iterative sequence of solution are obtained.     

EXISTENCE AND ITERATIVE APPROXIMATIONS OF BOUNDED POSITIVE SOLUTIONS TO A NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

In this paper,we consider a nonlinear neutral differential equation.By the Schauder fixed point theorem,some sufficient conditions are obtained to ensure the existence of uncountably many bounded positive solutions.In addition,we give the iterative approximation sequences with errors for these positive solutions and establish some error estimates between the approximate and the positive solutions.     

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.     

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,uniqueness, and multiplicity results on positive solutions for a class of Hadamard-type fractional boundary value problem on an infinite interval

This paper focuses on a class of Hadamard-type fractional differential equation with nonlocal boundary conditions on an infinite interval. New existence, uniqueness, and multiplicity results of positive solutions are obtained by using Schauder's fixed point theorem, Banach's contraction mapping principle, the monotone iterative method, and the Avery-Peterson fixed point theorem. Examples are included to illustrate our main results.     

分数阶微分方程的一些新结果

第一部分,介绍分数阶导数的定义和著名的Mittag—Leffler函数的性质．第二部分,利用单调迭代方法给出了具有2序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性和唯一性．第三部分,利用上下解方法和Schauder不动点定理给出了具有2序列Riemann—Liouville分数阶导数微分方程周期边值问题解的存在性．第四部分,利用Leray—Schauder不动点定理和Banach压缩映像原理建立了具有n序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性、唯一性和解对初值的连续依赖性．第五部分,利用锥上的不动点定理给出了具有Caputo分数阶导数微分方程边值问题,在超线性（次线性）条件下C310,11正解存在的充分必要条件．最后一部分,通过建立比较定理和利用单调迭代方法给出了具有Caputo分数阶导数脉冲微分方程周期边值问题最大解和最小解的存在性．     

一类二阶迭代泛函微分方程周期解的存在性

利用k-集压缩算子抽象连续性定理和一些分析技巧,研究了一类二阶迭代泛函微分方程周期解的存在性,得到了一些保证该类方程存在周期解的新结果.