Oscillation criteria for second order sublinear dynamic equations with damping term

This paper concerns the oscillation of solutions to the second order sublinear dynamic equations with damping. No sign conditions are imposed on coefficients. We illustrate the results by several examples.     

一类四阶奇异微分方程正解存在的充分必要条件

通过Green函数给出了一对具体的上下解,对一类奇异微分方程边值问题做了研究,得到正解存在的充分必要条件.     

Sublinear upper bounds for stochastic programs with recourse

Separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program. The resulting problem's objective involves the inf-convolution of convex functions. A dual of this problem is formulated to obtain an implementable procedure to calculate the bound. Function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables. The sublinear bound can often be used when other suggested upper bounds are intractable. Computational results indicate that the sublinear approximation provides good, efficient bounds on the stochastic program objective value.This research has been partially supported by the National Science Foundation. The first author's work was also supported in part by Office of Naval Research Grant N00014-86-K-0628 and by the National Research Council under a Research Associateship at the Naval Postgraduate School, Monterey, California.     

关于一个次线性逼近定理的新证法

Ｄｅｍｙａｎｏｖ和Ｒｕｂｉｎｏｖ在［１］中给出了一个次线性逼近定理．本文对该定理的证明进行了修正．     

一类四阶差分方程振动性的充分必要条件

本文给出了四阶差分方程△＾２（ｒｎ△＾２ｙｎ）＋ｆ（ｎ,ｙｎ）＝０,ｎ＝０,１,２,…的所有解（有界解）振动的一些充分条件和必要条件。     

The formulas for the representation of functions of two variables as a difference of sublinear functions

ABSTRACT

Having a function being a difference of sublinear functions defined on a plane, we present a formula for effective calculation of sublinear functions such that their difference is equal to the given one. Moreover, these newly calculated sublinear functions are minimal and as such unique-up-to-linear-summand. We also provide examples of such functions.     

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。     

次线性算子在加权Herz空间上的弱型估计

给出了一些次线性算子从加权Herz空间到加权弱Herz空间的有界性证明。