关于概率空间与次线性期望空间中的随机变量一致可积性的一个注记（英文）

在这篇注记中我们讨论随机变量的一致可积性.在概率空间中,我们引进了随机变量一致可积性的两个新的定义,并证明了他们与经典定义等价.在次线性期望空间中,我们给出了随机变量一致可积性的德拉瓦利普桑准则,并作了一些其它讨论.     

Forced oscillation of delay difference equations via nonprincipal solution

In this paper, we obtain a new oscillation result for delay difference equations of the form under the assumption that corresponding homogenous equation is nonoscillatory, where τ_n≤n+1. It is observed that the oscillation behaviormay be altered due to presence of the delay. Extensions to forced Emden‐Fowler–type delay difference equations in the sublinear (0<α<1) and the superlinear (1<α) cases are also discussed.     

Farkas’ lemma for separable sublinear inequalities without qualifications

We show that the celebrated Farkas lemma for linear inequality systems continues to hold for separable sublinear inequality systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinear programming problems which include classes of robust linear programming problems. We also deduce that the Lagrangian duality always holds for these programming problems without qualifications.     

Integral averages and oscillation of second order sublinear differential equations

New oscillation criteria are given for the second order sublinear differential equation

Order-Preserving Skew-Product Flows and Nonautonomous Parabolic Systems

The paper deals with order-preserving (or monotone) skew-product flows in Banach spaces. Within a general framework, we study long-time behavior of their trajectories. We introduce the concepts of equilibria, sub- and super-equilibria and we give simple conditions that guarantee their existence. Attention is mainly paid to order-preserving skew-product flows which have an additional concavity property called sublinearity, frequently encountered in applications. For these flows we prove the uniqueness and stability of equilibria and also a limit set trichotomy, stating that either (i) all orbits are unbounded, or (ii) all orbits are bounded but their closure reaches out to the boundary of the part, or (iii) there exists a unique, globally attracting equilibrium. Our main examples are quasilinear systems of parabolic equations with almost-periodic coefficients.     

零点有次线性项的椭圆问题的变号解

Abstract. It is proved that the semilinear elliptic problem with zero boundary value     

A Limit Set Trichotomy for Order-Preserving Random Systems

We study the asymptotic behavior of order-preserving (or monotone) random systems which have an additional concavity property called sublinearity (or subhomogeneity), frequently encountered in applications. Sublinear random systems are contractive with respect to the part metric, hence random equilibria are unique and asymptotically stable in each part of the cone. Our main result is a random limit set trichotomy, stating that in a given part either (i) all orbits are unbounded, or (ii) all orbits are bounded but their closure reaches out to the boundary of the part, or (iii) there exists a unique, globally attracting equilibrium. Several examples, including affine and cooperative systems, are given.     

一类 Rn 上半线性椭圆方程有界正解 的存在性和对称性

本文研究 Rn 上型如下列具有次线性项加超线性项椭圆方程: - Δu = a(x ) (λ us + up ) , x∈ Rn , 其中 ,n≥ 3, 0 < s < 1 < p,λ > 0为参数.用上下解方法给出了方程有界正解存在性及多解性结果.用移 动平面方法给出解的径向对象性结果 .     

一类分数阶p（x）-拉普拉斯方程的多重解

利用临界点理论、变分方法和分数阶变指数Sobolev空间理论, 研究带有非局部系数的分数阶p(x)-拉普拉斯方程边值问题的可解性。当非线性项在零点附近次线性或在无穷远处局部超线性增长时, 得到了此类问题多重解存在的充分条件。