Matrix characterization of oscillation for double sequences

The notion of oscillation for ordinary sequences was presented by Hurwitz in 1930. Using this notion Agnew and Hurwitz presented regular matrix characterization of the resulting sequence space. The primary goal of this article is to extend this definition to double sequences, which grants us the following definition: the double oscillation of a double sequence of real or complex number is given P-lim sup_{(m,n)→∞;(α,β)→∞}|S _m,n -S _α,β |. Using this concept a matrix characterization of double oscillation sequence space is presented. Other implication and variation shall also be presented.      

Oscillation of second order neutral delay differential equations of Emden-Fowler type

We present new oscillation criteria for the second order nonlinear neutral delay differential equation [y(t)-py(t-τ)]'+ q(t)y ^λ (g(t)) sgn y(g(t)) = 0, t ≧ t ₀. Our results solve an open problem posed by James S.W . Wong [24]. The relevance of our results becomes clear due to a carefully selected example. This revised version was published online in June 2006 with corrections to the Cover Date.     

Commutators of fractional integral operators on Vanishing-Morrey spaces

In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey spaces VL ^p,λ. In doing this we use an extension on Morrey spaces of an inequality by Fefferman and Stein concerning the sharp maximal function and the fractional maximal function and related Morrey inequalities.      

一阶中立型时滞差分方程振动的充分必要条件

研究了一阶常系数中立型时滞差分方程A[x(n)-px(n-τ)]+qx(n-σ)=0的振动性.通过构造若干适当的函数,分别得到了在01两种情况下该方程的一切解振动的充分必要条件.     

一类连续变量脉冲中立型差分方程

研究具连续变量脉冲中立型时滞差分方程△[y(t)-p(t)y(t-τ)]+q(t)y(t-σ)=0,t≠tky(tk+)-y(tk)=bky(tk),k=1,2,…利用辅助方程,建立等价定理,得到了方程解振动的显式充分性条件.     

偶阶半线性阻尼泛函微分方程的振动性

本文讨论了偶阶半线性阻尼泛函微分方程解的振动性质.利用广义Riccati变换和不等式技巧得到了所述方程的一切解均为振动的若干新的振动准则,推广和改进了一些文献中的结果.     

二阶非线性时滞差分方程解的振动性

研究了二阶非线性时滞差分方程△(α_n(△(x_n+p_nx_(n-r)))~γ)+bn(△(x_n+p_nx_(n-T)))~γ+f(n,x_(n-σ))=0给出方程振动的充分条件,推广和改进了中立时滞差分方程的许多结果.     

Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension

The persistence of subsonic phase boundaries in a multidimensional Van der Waals fluid is analyzed. The phase boundary is considered as a sharp free boundary that connects liquid and vapor bulk phase dynamics given by the isothermal Euler equations. The evolution of the boundary is driven by effects of configurational forces as well as surface tension. To analyze this problem, the equations and trace conditions are linearized such that one obtains a general hyperbolic initial boundary value problem with higher‐order boundary conditions. A global existence theorem for the linearized system with constant coefficients is shown. The proof relies on the normal mode analysis and a linear form in suitable spaces that is defined using an associated adjoint problem. Especially, the associated adjoint problem satisfies the uniform backward in time Kreiss–Lopatinski? condition. A new energy‐like estimate that also includes surface energy terms leads finally to the uniqueness and regularity for the found solutions of the problem in weighted spaces. Copyright © 2016 John Wiley & Sons, Ltd.     

ZEROS OF ENTIRE SOLUTIONS TO COMPLEX LINEAR DIFFERENCE EQUATIONS＊

In this article,we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations,and obtain some relations of the exponent of convergence of z...     

具有阻尼项的二阶自共轭矩阵微分系统的振动定理

运用Riccati技巧,正线性泛函和广义平均对方法,讨论具有阻尼项的二阶自共轭矩阵微分系统(P(t)Y’(t))’+r(t)P(t)Y’(t)+Q(t)Y(t)=0,t≥0,获得了一些新的振动定理.所得结果改进和推广了许多已知结论.特别地,补充了大量存在性结果,并能处理以前振动准则不能解决的问题.