Solutions to the system of operator equations AXB=C=BXA

In this paper, we present some necessary and sufficient conditions for the existence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB=C=BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.     

一类非线性算子方程的正解问题

研究算子方程X^s+A^*X^-tA=Q的正算子解的存在性问题,通过构造有效的迭代序列,给出了算子方程X^s+A^*X^-tA=Q有正算子解的一些充分条件和必要条件,同时给出了该方程有极大解和唯一解的条件.     

渐近线性算子方程的四种类型的解

利用拓扑度理论及不动点指数理论,讨论了渐近线性算子方程的四种类型的解(即零解、正解、负解和变号解)的存在性,并将这一抽象结果应用于微分方程两点边值问题.     

带$p$-Laplacian的四阶四点奇异边值问题的正解

In this paper, we consider the existence of positive solutions for the singular fourthorder four point boundary value problem with p-Laplacian operator. By using the fixed point theorem of cone expansion and compression, the existence of multiple positive solutions is obtained.     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel'skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.     

Existence and uniqueness of positive solutions of semilinear elliptic equations

This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained.     

一般Lidstone边值问题的n个正解的存在性

考察了含所有偶数阶导数的一般Lidstone边值问题的正解和对称正解.通过 选择合适的Banach空间和锥,对该问题建立了n个正解或者对称正解的存在性,其 中n是一个任意的自然数.基本工具是等价范数和锥拉伸与锥压缩型的Krasnosel'skii 不动点定理. 结论的主要条件是局部的.换言之,如果非线性项f在某些有界集上的 "高度"是适当的,则该问题可以具有n个正解.     

一类种群动力学模型正概周期解的存在性

本文讨论了一类时滞微分方程正概周期解的存在性问题,利用锥中u_0-凹算子与增算子的性质,不仅得到了上述系统的正概周期解的存在性与非存在性的结论,还改进了现有的结果,并且我们的方法也适用于更一般的系统．     

一类非线性算子方程的正算子解的研究

研究了算子方程X^(-1)+A(-1)+A⁺X+X^tA=Q,的正算子解问题,给出了此类非线性算子方程正算子解的范围以及正算子解存在的一些充分必要条件,并用迭代的方法得到了方程的正算子解.     

含有p-Laplacian算子的四阶奇异边值问题正解的存在性

研究了含p-Laplacian算子的奇异四阶四点边值问题,利用上下解方法与Schauder不动点定理,获得了至少一个C~3[0,1]正解的存在性结果.     

奇异二阶常微分方程组边值问题的正解

在与线性算子的谱半径相关的假设条件下,利用拓扑方法研究了一类奇异二阶常微分方程组边值问题,得到了正解的存在性.     

带有p-Laplacian算子模型的分数阶四点边值问题正解的存在性

研究了一类带有p-Laplacian算子的分数阶微分方程四点边值问题,利用不动点定理,得到了该边值问题至少存在一个正解的充分条件.     

一类算子方程的正算子解的研究

对算子方程X+A~*X~(-2)A=Q有正算子解的条件做了进一步的研究,得到了方程有正算子解时A,Q,X的范数、谱半径之间新的关系.并给出了算子方程X+A~*X~(-t)A=Q有正算子解的一些条件.     

算子方程X+A~*X~(-t)A=Q的正算子解的研究

研究了算子方程X+A*X~(-t)A=Q(t>1)的正算子解问题,分别给出了算子方程X+A*X~(-t)A=Q有正算子解的一些充分条件和必要条件,并确定了解的范围,用迭代的方法得到方程的正算子解.     

非正非线性算子方程正解的存在性及其应用

首先使用全局分歧理论得到了含参数非线性算子方程解集无界连通分支存在的结果,然后根据算子的正连通性得到了一类非正非线性算子方程正解的存在结果.使用本文的主要结果在无需假设非线性项为正的条件下可以得到某些微分边值问题正解的存在结果.     

带p-Laplace算子的奇异脉冲微分方程非局部边值问题

运用不动点指数理论,我们研究一类带p-L ap lace算子的奇异脉冲微分方程非局部边值问题正解的存在性.从本质上推广了已有文献的结果.     

Positive solutions of fractional differential equation boundary value problems at resonance

In this article, we study a class of fractional differential equations with resonant boundary value conditions. Some sufficient conditions for the existence of positive solutions are considered by means of the spectral theory of linear operator and the fixed point index theory.     

一类微分方程组的多重正解

本文讨论了 Ｂａｎａｃｈ空间中 Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题正解的存在性与多解性，通过线性算子的谱半径，给出其正解存在与多解的条件．     

Existence and uniqueness of positive solution for nonlinear fractional q-difference equation with integral boundary conditions

This paper studies a class of nonlinear fractional $q$-difference equations with integral boundary conditions. By exploiting the properties of Green"s function and two fixed point theorems for a sum operator, the existence and uniqueness of positive solutions for the boundary value problem are established. Iterative schemes for approximating the solutions are also obtained. Explicit examples are given to illustrate main results.