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.     

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.     

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.     

一类带有p-Laplacian算子的分数阶积分边值问题的正解与逐次迭代方法

本文研究一类带有p-Laplacian算子并且非线性项f中含有分数阶导数项的分数阶微分方程边值问题的正解的存在性.通过构造上解和下解并利用单调迭代方法,获得该边值问题存在正解的充分条件,并给出一个具体的例子作为应用.     

时标上二阶带p-Laplacian算子的脉冲边值问题单调迭代正解的存在性

论文利用单调迭代的方法证明了时标上二阶带p-Laplacian算子的脉冲边值问题的正解存在性.同时,举例阐述了主要结果.     

Banach空间中二阶非线性奇异微分方程多点无穷边值问题的正解

利用锥理论和Mōnch不动点定理结合单调迭代技巧,研究了Banach空间中一类二阶非线性奇异微分方程多点无穷边值问题,获得了正解的存在性定理和正解的迭代序列.     

一类具p-Laplacian算子的多点边值问题单调迭代正解的存在性

利用单调迭代的方法得到了一类具p-Laplacian算子的多点边值问题单调迭代正解的存在性,同时也得到了解的相应迭代序列.     

含p-Laplace算子的Sturm-Liouville边值问题正解的性质

研究了含p-Laplace算子的Sturm-Liouville边值问题正解的性质.利用p-Laplace算子的性质,使用L’Hpital(洛必达)法则和闭区间上连续函数的最值性定理,研究了含p-Laplace算子的Sturm-Liouville边值问题,得到了其正解存在的两个必要条件.最后给出了主要结论的应用.结论丰富了边值问题研究领域的内容,为利用计算机使用迭代技术求这类边值问题的近似解提供了新的渠道,推广了一些文献的结论.     

经由和型算子方法下共形分数阶微分方程正解的唯一性和迭代序列

本文研究了一类共形分数阶微分方程两点边值问题,通过利用定义在锥上的一类和型算子不定点定理,获得了微分方程正解存在唯一性,并构造一个迭代序列逼近唯一正解.最后,通过两个例子验证了本文获得的主要结论.     

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.     

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.     

Existence and iteration of monotone positive solutions for an elastic beam equation with a corner

This paper is concerned with the existence of monotone positive solutions for an elastic beam equation with a corner. The boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. By applying monotone iterative techniques, we not only obtain the existence of positive solutions, but also establish iterative schemes for approximating the solutions.     

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.     

Successive iteration and positive solutions for boundary value problem of nonlinear fractional q-difference equation

In this paper, we investigate the positive solutions for a class of nonlinear q-fractional boundary value problem. We not only obtain the existence and uniqueness of positive solutions, but also establish the iterative schemes for approximating the solutions, which is benefit for computation and application.     

A necessary and sufficient condition for the existence of symmetric positive solutions of higher-order boundary value problems

A necessary and sufficient condition is obtained for the existence of symmetric positive solutions to higher-order nonlinear boundary value problems. The uniqueness, an iterative sequence and an error estimation for symmetric positive solutions are also discussed. Moreover, we give an example to illustrate the applicability of our results. Our analysis mainly relies on the monotone iterative technique.     

Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces

In this paper, we introduce two iterative schemes for approximating solutions of generalized variational inequalities in the setting of Banach spaces. The existence of solutions of this general problem and the convergence of the proposed iterative schemes to a solution are established.