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Journal of Applied Mathematics and Physics 2023年第12期11卷 3914-3927页

作者： Xuefan Lin Weimin Hu youhui su Yongzhen Yun College of Mathematics and Statistics Yili Normal University Yining China School of Mathematics and Statistics Xuzhou University of Technology Xuzhou China Institute of Applied Mathmatics Yili Normal University Yining China

In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.

关键词： Fractional Differential Equation Fixed Point Theorem Existence of Solutions

Existence of Solutions for a Non-Autonomous Evolution Equations with Nonlocal Conditions

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Journal of Applied Mathematics and Physics 2023年第12期11卷 4079-4091页

作者： Lixin Sheng Weimin Hu youhui su Yongzhen Yun School of Mathematics and Statistics Yili Normal University Yining China School of Mathematics and Statistics Xuzhou University of Technology Xuzhou China Institute of Applied Mathematics Yili Normal University Yining China

The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.

关键词： Non-Autonomous Evolution Equation Nonlocal Conditions Mild Solution Evolution Family

A user-space file system for on-demand legacy desktop software

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Science China(Information Sciences) 2011年第6期54卷 1142-1150页

作者： ZHANG youhui 1,2 , su GeLin 1,2 & ZHENG WeiMin 1,2 1 Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China 2 Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China 1. Department of Computer Science and Technology Tsinghua University Beijing 100084 China2. Tsinghua National Laboratory for Information Science and Technology Tsinghua University Beijing 100084 China

Some user-level virtualization technologies have been used to convert legacy software (like the existing Windows desktop applications) into the on-demand software without any modification. To give the client a friendly and compatible method to access on-demand legacy software across the Internet, this paper presents a clientend file system for this usage case. It is a Windows user-space file system based on the cloud storage (where the on-demand software is stored), which converts the local file system accesses into remote visits. Quite a few optimizations are adopted and adjusted to suit the file-access-pattern of on-demand software, including the local cache, metadata/data/software prefetch and content-addressable storage (CAS), to decrease the number of remote visits and/or to overlap IO (input/output) operations with software execution. Detailed access-pattern analyses are also presented. This file system has been implemented and tests show that it is practical for much daily-used software-a local cache of limited size can provide up to 80% hit ratio and the corresponding overhead of running-time is about 37%. Owing to this method, on any compatible and networked computer, a user can use his/her personalized software conveniently although it does not exist on the local host.

关键词： on-demand software software as a service user-space file system cloud storage

一类非线性Caputo型分数阶微分方程耦合系统的正解

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吉林大学学报（理学版） 2017年第4期55卷 853-860页

作者：薛益民苏莹苏有慧徐州工程学院数学与物理科学学院江苏徐州221018

利用Schauder不动点定理、Leray-Schauder抉择理论和Banach不动点定理,研究一类含积分边值条件的非线性Caputo型分数阶微分方程耦合系统边值问题,得到了该耦合系统正解存在性和唯一性的充分条件,并举例说明定理的适用性.

关键词：分数阶微分方程耦合系统正解不动点定理

GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION

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Acta Mathematica Scientia 2005年第1期25卷 59-66页

作者：李万同张艳红苏有慧 Department of Mathematics Lanzhou University Lanzhou 730000 China Department of Mathematics Lanzhou University Lanzhou 730000 China Department of Mathematics Hexi University Zhangye 734000 China

In this paper the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].

关键词： Difference equation global attractivity stability equilibrium.

一类非线性项带导数的p-Laplacian边值问题正解的存在性和多解性

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应用数学学报 2023年第2期46卷 261-276页

作者：苏有慧孙文超孙爱徐州工程学院数学与统计学院徐州221018

本文研究了一类非线性项带导数的p-Laplacian算子的分数阶微分方程边值问题正解的存在性和多解性.首先,利用分数阶微分方程和边值条件给出了该边值问题的Green函数,然后利用Guo-Krasnosel’skii’s不动点定理和Leggett-Williams不动点... 详细信息

本文研究了一类非线性项带导数的p-Laplacian算子的分数阶微分方程边值问题正解的存在性和多解性.首先,利用分数阶微分方程和边值条件给出了该边值问题的Green函数,然后利用Guo-Krasnosel’skii’s不动点定理和Leggett-Williams不动点定理得出该边值问题一个或者三个正解的存在性结论.作为应用,给出两个例子验证了结论的适用性,特别是,用迭代法进行了逼近模拟,给出解的图形.值得一提的是此文研究的微分方程的非线性项是带有Riemann-Liouville型分数阶微分.

关键词：分数阶微分方程 p-Laplacian算子边值问题不动点定理

测度链上p-Laplacian边值问题的三个正对称解

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数学物理学报（A辑） 2008年第6期28卷 1232-1241页

作者：苏有慧李万同徐州工程学院数理学院徐州221008 兰州大学数学与统计学院兰州730000

该文研究了p-Laplacian动力边值问题(g(u~△(￡)))~▽+a(t)f(t,u(t))=0,t∈[0,T]_T,u(0)=u(T)=w,u~△(0)=-u~△(T)正解的存在性.其中叫是非负实数,g(v)=|v|^(p-2)v,p>1.根据对称技巧和五泛函不动点定理,证明了边值问题至少有三个正的对... 详细信息

关键词：测度链边值问题正对称解 P-Laplacian 不动点定理

一类具有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在唯一性

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数学物理学报（A辑） 2018年第6期38卷 1162-1172页

作者：贠永震苏有慧胡卫敏徐州工程学院数学与物理科学学院江苏徐州221000 伊犁师范学院数学与统计学院新疆伊宁835000

该文研究了一类具有p-Laplacian算子的非线性Caputo分数阶微分方程反周期边值问题解的存在唯一性.首先,利用分数阶微分方程和反周期边值条件给出了该边值问题的Green函数,然后利用p-Laplacian算子的性质和Banach压缩映射原理得到该边值... 详细信息

该文研究了一类具有p-Laplacian算子的非线性Caputo分数阶微分方程反周期边值问题解的存在唯一性.首先,利用分数阶微分方程和反周期边值条件给出了该边值问题的Green函数,然后利用p-Laplacian算子的性质和Banach压缩映射原理得到该边值问题解的存在唯一性结论,最后给出两个例子验证结论的合理性.值得一提的是此文研究的微分方程的反周期边值条件是带有Caputo分数阶微分.

关键词： Caputo分数阶微分反周期边值问题解的存在唯-性 p-Laplacian算子,Banach压缩映射原理

Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 349-412页

作者： Wenze su School of Mathematical Sciences Fudan UniversityShanghai 200433China

The author studies the 2D isentropic Euler equations with the ideal gas *** exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar *** solutions to the 2D isentropic Euler equations are associated with non-zero vorticity at the shock and have uniform-in-time-1/3-Holder ***,these point shocks are of self-similar type and share the same profile,which is a solution to the 2D self-similar Burgers *** proof of the solutions,following the 3D construction of Buckmaster,Shkoller and Vicol(in 2023),is based on the stable 2D self-similar Burgers profile and the modulation method.

关键词： 2D isentropic Euler equations Shock formation Self-similar solution

一类非线性分数阶积分微分方程解的存在性与模拟仿真

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吉林大学学报（理学版） 2021年第4期59卷 828-836页

作者：孙文超苏有慧孙爱沈阳工业大学理学院沈阳110870 徐州工程学院数学与统计学院江苏徐州221018

首先,用Banach压缩映射原理和Krasnoselskii不动点定理研究一类非线性分数阶积分微分方程解的存在性,得到了其至少存在一个解和存在唯一解的结果;其次,通过迭代法对两个实例进行模拟仿真验证所得结果.

关键词：分数阶积分微分方程模拟仿真存在性迭代法