Separately continuous selectors

The existence of separately continuous selectors of a separately lower and upper semicontinuous many-valued multivariate map is proved, provided its domain is a compact set and its range is a convex closed subset of a metrizable convex compact set. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 209–216, February, 1998. This research was partially supported by the Russian Foundation for Basic Research under grant No. 93-01-00264.     

Kamenev-type oscillation criteria for delay difference equations

Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation Δ(pn(Δ(xn cnxn-τ))γ) qnxβn-σ=0,n=0,1,2…which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].     

二阶强次线性泛函微分方程解的振动性质

讨论了一类二阶强次线性泛函微分方程解的振动性质,获得了三个新的振动性定理,推广和改进了Grace和Lalli(J.Math.Anal.Appl,1987,123,584—588)的结果.     

次线性算子在齐型空间上的Herz空间上的有界性

获得了一些关于次线性算子在较弱的局部尺寸条件下在齐型空间上的Herz(弱Herz)空间上的有界性的一般性的结果.     

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATION OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

1 IntroductionRecently there wele a lot of activity concerning the oscillatory behavior ofsolutions of delay differential equations. We refer to the monographs [1,2,3,4].In particular, the oscillations and nonoscillations of solutions of the first orderneutral linear differential equation[x(t) -- p(t)x(t -- T)]' Q(t)x(t -- a) = 0 (*)have been investigated by many authors.In this paper, we consider the following first order nonlinear neutral diffe-rential equationwhereT) a E (0, co), al(t) …     

一类二阶强次线性微分方程的振动性定理

讨论了一类二阶强次线性微分方程解的振动性质,获得了三个新的振动性定理,推广和改进了相关文献的结果.     

向量值算子在空间上的有界性

研究了向量值Hardy-Litlewood算子在Herz-Morrey及弱Herz．Morrey空间上的有界性．应用这些结果。得到了一大类定义在R^n上的次线性算子向量值不等式．     

Nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity

We are concerned with existence, nonexistence and multiplicity of nonnegative solutions for the elliptic problem

     

Belohorec‐type oscillation theorem for second order sublinear dynamic equations on time scales

Consider the Emden‐Fowler sublinear dynamic equation (0.1) where $p\in C(\mathbb{T},R)$, where $\mathbb{T}$ is a time scale, 0 < α < 1. When p(t) is allowed to take on negative values, we obtain a Belohorec‐type oscillation theorem for (0.1). As an application, we get that the sublinear difference equation (0.2) is oscillatory, if and the sublinear q‐difference equation (0.3) where $t\in q^{\mathbb{N}_0}, q>1$, is oscillatory, if      

关于容度下Borel-Cantelli引理的一点注记

这个注记中我们证明了在没有两两独立假设条件下对容度的Borel-Cantelli引理,获得了容度对并事件的最优下界.这些结果推广了经典的Borel-Cantelli引理.