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Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion

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Applied Mathematics(A Journal of Chinese Universities) 2019年第2期34卷 184-204页

作者： FEI Chen FEI Wei-yin YAN Li-tan Glorious Sun School of Business and Management Donghua UniversityShanghai200051China School of Mathematics and Physics Anhui Polytechnic UniversityWuhuAnhui 241000China

Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper, by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.

关键词： stochastic differential delay equation (SDDE) sublinear expectation existence and uniqueness G-Brownian motion stability and boundedness

O(1/t) complexity analysis of the generalized alternating direction method of multipliers

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Science China Mathematics 2019年第4期62卷 795-808页

作者： Xingju Cai Deren Han School of Mathematical Sciences and Key Laboratory for Numerical Simulation of Large Scale Complex Systems of Jiangsu Province Nanjing Normal University

Owing to its efficiency in solving some types of large-scale separable optimization problems with linear constraints, the convergence rate of the alternating direction method of multipliers(ADMM for short) has recently attracted significant attention. In this paper, we consider the generalized ADMM(G-ADMM), which incorporates an acceleration factor and is more efficient. Instead of using a solution measure that depends on a bounded set and cannot be easily estimated, we propose using the original ?-optimal solution measure, under which we prove that the G-ADMM converges at a rate of O(1/t). The new bound depends on the penalty parameter and the distance between the initial point and the solution set, which is more reasonable than the previous bound.

关键词： generalized alternating direction method of multipliers separable convex optimization iteration complexity sublinear convergence rate

KAMENEV-TYPE OSCILLATION CRITERIA FOR DELAY DIFFERENCE EQUATIONS

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Acta Mathematica Scientia 2007年第3期27卷 574-580页

作者：程金发 Department of Mathematics Xiamen University

Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ）＋ qnX^Bn-σ = 0, n ：0, 1, 2...wh... 详细信息

关键词： Oscillation superlinear sublinear difference equations

The decomposition of weighted Herz space on R^n and its applications

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Science China Mathematics 1995年第2期38卷 147-158页

作者：陆善镇杨大春 Department of Mathematics Beijing Normal University Beijing 100875 China

The decompositional characterizations of the weighted Herz spaces on Rn are established. Using this decomposition, the boundedness on the weighted Herz spaces for a large class of sublinear operators is studied.

关键词： weight unit Herz space Hardy space sublinear operator.

On the Existence of Positive Solution for n OrderSingular Boundary Value Problems

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Chinese Quarterly Journal of Mathematics 1998年第3期13卷 68-73,页

作者： Shi Guoliang (Jinan School of Petrochemical Economy,Shandong,Jinan,250101) 济南石化经济学校山东济南 250101

In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 00,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.

关键词： singular BVP superlinear sublinear positive solution cone

EXISTENCE OF POSITIVE SOLUTIONS TO(n-1,1)CONJUGATE BOUNDARY VALUE PROBLEMS

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Annals of Differential Equations 1998年第3期14卷 511-517页

作者：蒋达清王艳刘辉昭东北师范大学 130024 黑龙江省财政专科学校 150028 哈尔滨师范大学 150080

In this paper, we restablish the existence of positive solution to (n - 1, 1)conjugate boundary value problemIt permits a(t) = 0 on some subintervals of [0, 1] and to have singularity at t = 0and t = 1.

关键词： Boundary value problem superlinear sublinear cone

Existence and Concentration of Solutions for An Indefinite Schrodinger-Kirchhoff System

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Chinese Quarterly Journal of Mathematics 2020年第1期35卷 37-45页

作者： CHEN Yu-song CHANG He-jie Ministry of Basic Education Shangqiu Institute of TechnologyHenan Shangqiu 476300China Ministry of Basic Education Luohe Vocational Technology CollegeHenan Luohe 462000China

This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a *** require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational ***,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as *** is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more *** overcome this difficulty,we adopt different method.

关键词： Schrodinger-Kirchhoff system sublinear Variational methods Concentration